UV LED BASED CHARGE CONTROL FOR THE LISA …

UV LED BASED CHARGE CONTROL FOR THE LISA GRAVITATIONAL REFERENCE SENSOR

By

TAIWO JANET OLATUNDE

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2018

To Yomi. Ore mi. Ololufe.

4

ACKNOWLEDGMENTS

When I started at the University of Florida in the spring of 2012, it was my first

time outside of my country of birth and I was in great need of a support network to help

me thrive. I met Dr. John Conklin at the end of the Fall 2012 semester and started

working with him and other members of the Precision Space Systems Lab (PSSL)

group in 2013. What a blessing that turned out to be! He not only provided the guidance

I needed as far as translating theoretical classroom knowledge into real hands-on

situations in the lab, he was also very supportive. He wanted me to succeed.

Many thanks to the other members of My PhD dissertation Committee; Dr. Peter

Wass, Dr. George Sawyer and Dr. Guido Mueller for their valuable feedback and for

letting me use resources available to them when I needed to.

I want to express my appreciation for the financial support that made the work

presented in this Dissertation possible, specifically, the NASA N.G. Roman Tech

Fellowship, grant number NNX15AF26G.

I would like to thank members of the PSSL group and the LISA group for the

warm, welcoming work environment and their friendship. I must mention Dr. Guido

Mueller, Paul Serra, Nathan Barnwell, Seth Nydam, Stephen Apple, Tyler Ritz, Daniel

Hillsberry, Samantha Parry, Deep JariwaIa, Thida Pechsiri, Benjamin Letson, Henri

Inchauspe and Myles Clark. Special thanks to Paul Serra for spending several weeks

with me on UV LED fiber coupling and the design of the UV LED driver board,

Samantha Parry for helping with further board testing, Stephen Apple for helping me get

a better understanding of the pendulum and for helping to analyze charge measurement

5

data. I am grateful to Nicholas Turetta and Henri Inchauspe for working with me on the

charge control model.

To my husband: Yomi, I need you. Thank you for your patience and sacrifice my

love. To my children: Mayowa Katherine and Ayomide Joanne, I am always excited to

see you after a day of hard work. Thank you for brightening every aspect of my

existence. Life was certainly not this interesting before you both came along. I also want

to acknowledge my parents, Esther Binsola Talabi and Olubiyi Joseph Talabi for their

words of encouragement.

I am fortunate to have had the opportunity to experience the wonderful and

inclusive environment that the University of Florida provides.

6

TABLE OF CONTENTS

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF TABLES ............................................................................................................ 8

LIST OF FIGURES .......................................................................................................... 9

LIST OF ABBREVIATIONS ........................................................................................... 13

ABSTRACT ................................................................................................................... 14

CHAPTER

1 INTRODUCTION .................................................................................................... 16

1.1 LISA- A Developing Gravitational Wave Observatory ....................................... 19 1.2 LISA Requirements ........................................................................................... 21

1.3 Gravitational Reference Sensor ........................................................................ 23 1.4 Charge Control on LISA Test Masses ............................................................... 24 1.5 Summary of Chapters ....................................................................................... 25

1.6 Contributions ..................................................................................................... 28

2 UV LEDS FOR LISA TEST MASS CHARGE CONTROL ....................................... 30

2.1 Hg Lamps vs. UV LEDs .................................................................................... 30 2.2 UV LED Testing ................................................................................................ 31

2.2.1 UV LED Fiber Coupling and Electronics Driver Board for Charge Control........................................................................................................... 33

2.2.2 Proposed Heat Dissipation Management ................................................ 35

2.3 Performance of UV LED Driver Board .............................................................. 35

3 QUANTUM YIELD AND REFLECTIVITY OF LISA TEST MASSES ...................... 37

3.1 Motivation for Measuring QY and Reflectivity ................................................... 37 3.2 Reflectivity Analysis for Two Infinite Parallel Plates .......................................... 37 3.3 QY Experimental Set up and Apparatus Description ........................................ 41

3.3.1 QY Dependence on Energy of Emitted UV Light .............................. 42

3.3.2 QY Measurements and Wavelength ................................................. 44 3.3.3 QY Measurements vs. Time .............................................................. 45 3.3.4 QY After a Bake-out .......................................................................... 46

3.3.5 Sample Preparation, Cleaning and Storage ...................................... 49 3.3.6 Evaluating the QYs of Commercially Polished Au Surfaces .............. 52 3.3.7 Investigating QY Dependence on Pressure ...................................... 53

3.5 Summary of QY Measurements ........................................................................ 59 3.6 Alternative Coatings Explored ........................................................................... 64

7

3.7 X-ray Photoelectron Spectroscopy Measurements ........................................... 65

3.8 Conclusions ...................................................................................................... 69

4 DEMONSTRATION OF DC AND AC UV LED CHARGE CONTROL ON THE UF TORSION PENDULUM ..................................................................................... 72

4.1 Pendulum Description ....................................................................................... 72 4.1.1 Capacitive and Interferometric Readout .................................................. 76 4.1.2 Measured Time Series of The Pendulum Rotation Angle ........................ 77 4.1.3 Pendulum Acceleration Noise Performance ............................................ 79

4.2 Electrostatic Force acting on the Pendulum’s Test Masses and Charge Measurement ....................................................................................................... 81

4.3 Analytical Charge Control Model for the LISA GRS ...................................... 84 4.3.1 The Pendulum GRS as a Simplified Parallel Plate Circuit ....................... 85

4.3.2 Photoelectron Energy Distribution ........................................................... 88 4.3.3 Implementing The Charge Control Model in MATLAB ............................. 94

4.4 DC Charge Control Demonstration on the UF Torsion Pendulum .................... 95 4.5 AC Charge Control With The UF Torsion Pendulum......................................... 96

4.5.1 AC Charge Control Experiments With Varying UV Phase ................... 99 4.5.2 Measuring Saturation Voltage as a Function of UV Light Injection ........ 100 4.5.3 Charge Rate .......................................................................................... 103

4.6 Fitting Analytical Charge Control Model to Data .......................................... 105

4.6.1 Case 1: 𝒏𝒕𝒐𝒕 (𝑽𝒊𝒏𝒋 , 𝑽𝑻𝑴 = 𝟎) .............................................................. 105

4.6.2 Case 2: 𝑽𝑻 (𝑽𝒊𝒏𝒋 , 𝒕 = ∞) ...................................................................... 110

4.6.3 Case 3: 𝒏𝒕𝒐𝒕 (𝑽𝒊𝒏𝒋 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕, 𝑽𝑻𝑴) ............................................... 112

4.7 Conclusions .................................................................................................... 115

5 SUMMARY OF CONCLUSIONS INCLUDING RECOMMENDATIONS FOR FUTURE WORK ................................................................................................... 117

APPENDIX

A DISTRIBUTION OF ELECTRON ENERGIES AS A FUNCTION OF APPLIED BIAS VOLTAGE .................................................................................................... 121

B SOLUTIONS TO PHOTOELECTRON FLUX EQUATIONS .................................. 123

C CHARGE MEASUREMENT EQUATIONS ........................................................... 127

LIST OF REFERENCES ............................................................................................. 131

BIOGRAPHICAL SKETCH .......................................................................................... 134

8

LIST OF TABLES

Table page 3-1 Quantum Yield Measurements from Au samples coated from March 2013

through August 2017, refer to Figures 3-4 through 3-14 ..................................... 59

3-2 XPS measurements for bare Au sample cleaned with isopropanol ......................... 66

3-3 XPS measurements for Au sample treated with Thiol. ............................................ 67

9

LIST OF FIGURES

Figure page 1-1 A gravitational wave propagating orthogonally to the detector plane and

linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave; these length changes are reversed during the other half-cycle. The output photodetector records these differential cavity length variations.. ........... 18

1-2 Key results of the analysis of GW150914, comparing the reconstructed gravitational-wave strain with the predictions of the best matching waveform computed from general relativity, over the three stages of the event; inspiral, merger and ring down. Also shown are the separation and velocity of the black holes, and how they change as the merger event unfolds ........................ 19

1-3 LISA’s nominal configuration .............................................................................. 20

1-4 The LISA technology package (ESA/ATG media lab, LISA L3 mission proposal) ............................................................................................................ 22

1-5 Sensitivity curve showing gravitational wave sources in the LISA frequency range compared with its sensitivity for a three arm configuration ....................... 23

1-6 Flight-like GRS ................................................................................................... 24

2-1 Left: fiber coupled TO18 UV LEDs from SETi, Right: Intensity spectrum of 240 and 250 nm UV LEDs compared with the work function of Au and the Hg lamp discharge wavelength ................................................................................ 30

2-2 Left: IV curve for TO18 UV LED, Right: PI curve for TO18 UV LED.................... 32

2-3 Left: IV curve for 240 nm TO39 BL and HS, Right: PI curve for 240 nm TO39 BL and HS .......................................................................................................... 32

2-4 Left: 240 nm TO39 BL UV LEDs, Right: 250 nm TO39 BL UV LEDs .................. 32

2-5 Output optical power of TO39 UV LED after being mechanically fiber coupled . 33

2-6 Heat dissipation management design ................................................................ 34

2-7 UV LED driver board assembled with the UV LED inside a box ........................ 34

2-8 Average power output of UV LED driver board for a 5 – 20 mA current setting input and a constant 5 % duty cycle ................................................................... 36

2-9 Average power output of UV LED driver board for various duty cycle settings .. 36

3-1 Reflections between two surfaces with different QYs and similar reflectivities ... 38

10

3-2 Reflections between two surfaces with different QYs and different reflectivities ......................................................................................................... 40

3-3 QY measurement apparatus set up in large vacuum at ~3 × 10 − 6 Torr, QY apparatus was subsequently set up in the small vacuum chamber with a leak valve for pressure adjustments ........................................................................... 42

3-4 QY of Au samples at 240 nm > QY at 250 nm ................................................... 45

3-5 Successive QY measurements with sample 1DP held at 10 − 5 Torr using a UV wavelength of 240 nm .................................................................................. 46

3-6 Measured QY on Au sample 2BP with bake-out at 130˚C and 240 nm .............. 46

3-7 Fraction of light reflected as a function of angle of incidence (in degrees) for

254 nm wavelength showing the two polarization components Rp and Rs comparing results described by Daniel Hollington (Dissertation 2011) and Johnson and Christy (1972). .............................................................................. 48

3-8 QY with detailed cleaning procedure and bake-out at 130°C using 240 nm UV LEDs for sample 1CP ......................................................................................... 51

3-9 QY with detailed cleaning procedure and bake-out at 130°C with UV wavelengths of 240 nm vs. 250 nm for sample 1AP ........................................... 51

3-10 QY of Commercially polished sample 4AP measured at 130°C with a 240 nm

at ~2x10 − 6 Torr ................................................................................................ 53

3-11 QY of sample 4AP measured between 10-8 and 10-6 Torr ................................ 57

3-12 QY of sample 4BP measured between 10-8 and 10-6 Torr ................................ 57

3-13 QY of sample 4CP measured between 10-8 and 10-6 Torr ................................ 58

3-14 QY of sample 4DP measured between 10-8 and 10-6 Torr ................................ 58

3-15 Long term QY measurements of sample 4CP at 10-8 Torr ................................ 59

3-16 Results of QY as a function of pressure at 240 nm ............................................. 60

3-17 Results of QY as a function of pressure at 250 nm ............................................. 60

3-18 Left to right; Aluminum substrates, hand-polished and coated with Au, TiC and SiC ............................................................................................................... 64

3-19 Results of QY measurements for Au, TiC and SiC coatings .............................. 67

3-20 The XPS measurements of bare Au cleaned with isopropanol .......................... 69

11

3-21 XPS measurement spectrum of Au after being treated in thiol solution for 24 hours .................................................................................................................. 68

4-1 Pendulum inertial member surrounded by electrostatic shields, Simplified electrode Housing, CAD model of the torsion pendulum, Torsion pendulum assembly enclosed inside the vacuum chamber ................................................ 73

4-2 UV light injection geometry for the simplified GRS, Left: UV light illuminates either the TM or the electrodes, Right: UV light simultaneously illuminates both the TM and injection electrodes .................................................................. 74

4-3 Test mass rotation and test mass swing ........................................................... 75

4-4 Capacitive and Interferometric read-out scheme, Actuation and capacitive sensing scheme for a pair of electrodes enclosing a single TM, Electrostatic actuation electronics, Interferometric readout scheme for TM position, Layout of interferometer components in the torsion pendulum ....................................... 77

4-5 Pendulum angle as a function of time as measured both capacitively and interferometrically ............................................................................................... 78

4-6 UF torsion pendulum acceleration noise spectrum ............................................ 79

4-7 LISA requirements compared with the acceleration noise performance of the torsion pendulum facility ..................................................................................... 80

4-8 Left: TM position with respect to the electrodes, Right: Suspended pendulum

showing the force Fx in the direction of the sensitive axis ................................... 81

4-9 Pendulum angle as a function of time during charge measurement on the pendulum ............................................................................................................ 84

4-10 Simplified circuit model for charge control ........................................................... 88

4-11 Electron exchange in a parallel plate configuration ............................................ 89

4-12 Distribution of energies of emitted electrons in a parallel plate configuration ..... 90

4-13 Straight line approximation of the distribution of energies .................................. 91

4-14 Pendulum charge during DC charge control operations on the UF torsion pendulum ............................................................................................................ 96

4-15 Left: UV LED emission out of phase with respect to the injection signal Right: UV LED emission in phase with respect to the injection signal .......................... 96

4-16 Test mass potential during AC charge control experiment ................................. 98

12

4-17 TM Potential while illuminating the AC port with pulsed UV light while varying the phase with respect to the injection voltage. ................................................ 100

4-18 Saturation voltage Vs. UV light phase using the electrodes port ...................... 101

4-19 Saturation voltage Vs. UV light phase using the TM port ................................. 102

4-20 Saturation voltage Vs. Phase using the TM-Injection electrodes port .............. 102

4-21 TM voltage as a function of time when using the TM port and EH port to move the voltage due to charge on the TM positive and negative .................... 104

4-22 UV light injection geometry and circuit model for calculating 𝑛𝑡𝑜𝑡 with varying 𝑉𝑖𝑛𝑗 and 𝑉𝑇𝑀 = 0 ............................................................................... 105

4-23 Measured test mass charge rate versus the potential barrier and the best fit model for the electrodes port ............................................................................ 106

4-24 Measured test mass charge flow rate as a function potential barrier for each surface when UV light is directed towards the electrodes ................................ 107

4-25 Measured charge rate vs. phase using the TM port and best fit model to the data .................................................................................................................. 109

4-26 Measured charge flow rate for each surface from TM port and best fit model . 109

4-27 TM Voltage at equilibrium for different values of the potential barrier on the electrodes port .................................................................................................. 111

4-28 TM Voltage at equilibrium for different values of potential barrier when using the TM port ....................................................................................................... 111

4-29 Circuit model showing the TM voltage as a contribution of the voltage due to charge and the TM polarization due to the injection voltage ............................. 112

4-30 Voltage time series as TM voltage approaches saturation from below ............. 112

4-31 Voltage time series as TM voltage approaches saturation from above ............. 112

4-32 Measured charge flow rate and best fit model as test mass voltage changes at a constant potential bias when using the electrodes housing port ................ 114

4-33 Charge flow rate as the test mass voltage changes at a constant potential bias when using the TM port .................................................................................... 115

13

LIST OF ABBREVIATIONS

Au

BL

EH

ESA

FOC

GRS

Hg

HS

LISA

LPF

NASA

ODE

TEC

TM

UV LED

Gold

Ball Lens

Electrode Housing

European Space Agency

Fiber Optic Cable

Gravitational Reference Sensor

Mercury

Hemispherical Lens

Laser Interferometer Space Antenna

LISA Pathfinder

National Aeronautics and Space Administration

Ordinary Differential Equation

Thermo Electric Cooler

Test mass

Ultra Violet Light Emitting Diode

14

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

UV LED BASED CHARGE CONTROL FOR THE LISA GRAVITATIONAL REFERENCE

SENSOR

By

Taiwo Janet Olatunde

December 2018

Chair: John W. Conklin Major: Aerospace Engineering

Test masses in the Laser Interferometer Space Antenna (LISA) must maintain

residual test mass accelerations under 3 fm/s2/√Hz at all frequencies between 0.1 mHz

and 3 mHz. Charge build-up on the test masses couples to stray electrical potentials and

external electromagnetic fields to contribute to unwanted force noise which mask

gravitational wave signals. The currently proposed discharge system for LISA follows

the LISA Pathfinder (LPF) discharge system which used the photoelectric effect to

transfer electrons from the test masses to the space craft and vice versa. In LPF the

required UV-photons were generated by a Hg-discharge lamp (254 nm) while the plan

for LISA is to use Ultra Violet Light Emitting Diodes (UV LEDs). These UV LEDs have a

lower mass, higher power efficiency and their photon energy often exceeds the work

function of pure gold.

The Quantum Yield, calculated as the number of electrons ejected from the

surface divided by the number of incident photons, is one of the essential properties

controlling the charge control system. Evaluated spectral properties for fiber coupled UV

LEDs manufactured by Sensor Electronic Technology (SETi), performed at the

15

University of Florida shows that the wavelength of the 240 nm UV LED peaks at a value

that is closer to the work function of Au and is less sensitive to surface properties.

Experimental results of long term yield measurements on Au samples as a

function of wavelength showed 240 nm UV LEDs consistently outperforming 250 nm UV

LEDs in Quantum Yield by more than a factor of two with or without a bake-out. Using

240 nm UV LEDs for the charge control scheme in LISA would reduce the need to rely

on probable contamination of the Au samples for a lowering of work functions which

allow higher wavelengths and lower energy UV LEDs to be used.

The discharging of the test masses in LPF was done at DC. This involved

Illuminating the test mass or the electrode housing irrespective of voltages applied on

the electrodes. Illuminating the test mass resulted in a more positive test mass charge

while illuminating the electrode housing made the test mass charge more negative. AC

charge control is a new scheme being studied as an alternative to the DC charge

control system. In this case, the output of the UV light is modulated with respect to the

voltage on the electrodes. This work addresses the results of AC and DC charge control

modes demonstrated on the University of Florida torsion pendulum.

For AC charge control in the torsion pendulum, the output of a 240 nm UV LED

was pulsed with respect to the 100 KHz injection signal already present in the simplified

Gravitational Reference Sensor (GRS). Key results show that test mass charge can be

controlled at AC by setting the phase of the UV LED output at a particular value with

respect to the injection. The set phase depends on whether the UV light is illuminating

the TM, the EH or both simultaneously. The need to have three different ports for the

UV Injection scheme in LISA is removed but could still be useful for redundancy.

16

CHAPTER 1 INTRODUCTION

Albert Einstein concluded in 1915 that spacetime deforms in the presence of

massive objects by bending like an elastic fabric, a lighter object moving along a path

nearby does not just continue, it is rerouted and pulled into the curve created by the

heavier object. The solar system gives a perfect example of the curvature of space

mainly due to the Sun; the other planets are not being pulled towards it, they just follow

the curved space time distortion it creates. When the curvature created in space time by

a heavy object such as a star becomes extreme, the gravitational pull, which is

proportional to the inverse square of the distance between them (GMm

r2 ), is very strong for

objects that are close enough. They are pulled in and never escape. Objects at longer

distances experience a weaker gravitational pull since the distance between them is

increased by a factor raised to the second power. For instance, a factor of four increase

in separation distance will lead to a reduction in the gravitational pull by a factor of

sixteen.

Two objects orbiting each other create a dynamic curvature in space-time by

their movements, this results in little ripples through the universe known as gravitational

waves. The waves cause variations in the apparent distance between free-falling

objects with a very small relative amplitude that makes them difficult to detect. The

violent collision or merger of two massive objects such as black holes or neutron stars

produces the strongest gravitational waves. At typical cosmological distances, even the

most powerful gravitational waves create strain amplitudes which are only of the order

of ~10-21. If the distance between two reference test masses in free fall is measured by

means of an interferometer, a gravitational wave moving in a direction that is not aligned

17

with the space between them would alter the amplitude of their separation with a

displacement comparable to the amplitude of the gravitational wave.

The discovery in 1974, of a pulsar in orbit with a neutron star by Russell Hulse

and Joseph Taylor (PSR1913+16) [1] was taken as an indirect evidence of the

existence of gravitational waves. On September 14, 2015, the first direct detection of

gravitational waves was made by the Laser Interferometer Gravitational-wave

Observatory (LIGO) at Hanford, Washington and Livingston, Louisiana. Both

observatories detected gravitational wave signal GW150914, produced by the merger of

two black holes each several times the mass of the sun. LIGO detectors are modified

versions of the Michelson Interferometer [25]. In the original version of the Michelson

Interferometer, light from a source is passed through a beam splitter to create two

beams of light moving towards mirrors that reflect them back such that they recombine

at the beam splitter. The recombined beams form an interference pattern which

depends on the arm length difference. Any change of the arm length difference will

modulate the interference pattern and create a measurable change in the intensity

leaving the interferometer. Included in each LIGO arm are two 40 kg fused silica mirrors

with longer separation distances of 4 km apart and ‘Fabry Perot Cavities’ added for

increased sensitivity. The optical system in LIGO is installed in a vacuum system

covering about 16 km at a pressure of 10−8 Torr to eliminate likely disturbances from

dust, sound waves, temperature variations and air currents which would make

gravitational wave detection impossible [26]. Figure 1-1 shows the key elements of the

LIGO detector.

18

Figure 1-1. A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave; these length changes are reversed during the other half-cycle. The output photodetector records these differential cavity length variations. Inset (a): Location and orientation of the LIGO detectors at Hanford, WA (H1) and Livingston, LA (L1). Inset (b): The linear spectral density of the equivalent gravitational wave strain noise near the time of the first detection.

The need for LIGO to be able to detect the motion of the test masses due to a

passing gravitational wave requires that environmental interferences be eliminated. This

is done through active systems that correct disturbing movements in real time and

passive damping systems that hold the mirror test masses via a suspension system

made up of four pendulums. Laser beams are incident on one side of the system while

the other side helps to steady the mirrors for disturbances not associated with space.

This ensures that the mirrors remain in the free fall condition required for gravitational

19

wave detection while sensors and actuators control the position and orientation of the

test masses [27]. Figure 1-2 gives the analysis of GW150914. Both pictures were

obtained from the LIGO scientific collaboration [2].

Figure 1-2. Key results of the analysis of GW150914, comparing the reconstructed gravitational-wave strain with the predictions of the best matching waveform computed from general relativity, over the three stages of the event; inspiral, merger and ring down. Also shown are the separation and velocity of the black holes, and how they change as the merger event unfolds

1.1 LISA- A Developing Gravitational Wave Observatory

LIGO is limited to observing objects in the frequency range of 10 Hz to 1000 Hz.

A detector capable of observing lower frequency gravitational waves with longer

wavelengths makes the case for a space based detector such as the Laser

20

Interferometer Space Antenna (LISA) which will observe in the low frequency range of

the gravitational wave spectrum between 0.1 mHz and 1 Hz.

Figure 1-3. LISA’s nominal configuration

LISA will be a space based gravitational wave observatory that will use laser

interferometry to measure changes in separations between isolated test masses caused

by gravitational wave induced strains in space time. LISA requires test mass (TM)

accelerations to be suppressed below 3 fm /𝑠2 /√Hz at all frequencies between 0.1 mHz

and 3 mHz. It is made up of three spacecraft flying in equilateral triangle formation as

illustrated in Figure 1-3 [3]. There are two test masses per spacecraft, free in one axis

each and acting as end mirrors for the interferometry measurements. Arm lengths; L1,

L2 and L3 are interferometer arms with lengths of 2.5 million kilometers each.

21

Each TM in the spacecraft is enclosed in an electrode housing that supports the

sensing electrodes and protects the TM from many disturbances including solar wind

and high energy particles from galactic and solar rays. However, some of them can still

penetrate and charge the TMs. The caging and uncaging process may also leave a

charge on the TMs. Charge accumulation on the TM will cause its potential to vary and

result in an electrostatic attraction towards the surrounding [14]. Test mass charge also

couples to imbalanced DC biases on opposing conductors of the housing to produce

random walk force noise [4, 5].

1.2 LISA Requirements

Strains produced by the strongest gravitational waves are on the order of ~10−21

therefore LISA relies on the ability of laser interferometers to accurately measure the

displacement between two free falling test masses in opposing spacecraft on the order

of a picometer. An obvious challenge to this is the elimination of unwanted forces acting

on the TM that could mask TM accelerations that are only due to gravitational waves.

LISA Pathfinder (LPF), shown in Figure 1-4 was launched on December 3 2015.

It is a joint European Space Agency (ESA) and National Aeronautics Space

Administration (NASA) mission intended to demonstrate many of the technologies

required for LISA such as drag free control, inertial sensors and precision laser

interferometry [6]. One key difference between LPF and LISA is that the sensitive axes

of the two TMs in LPF lie on the same straight line and since they are both located in a

single spacecraft which cannot follow the trajectories of both TM along the same degree

of freedom, one of them has to be electrostatically controlled to follow the other [32].

The TMs in LISA will be located in two separate spacecrafts 2.5 million kilometers apart.

22

Figure 1-4. The LISA technology package (ESA/ATG media lab, LISA L3 mission proposal)

LISA pathfinder has demonstrated that a TM can be maintained in the free fall

condition needed for gravitational wave detection. The performance is related to the low

frequency side of the sensitivity curve and is related to acceleration noise. Acceleration

noise in the LISA GRS is due to various uncontrolled forces that could mimic or mask a

gravitational wave signal. For this reason, acceleration noise measurements are used to

assess the performance of the system and allow for the identification and mitigation of

possible sources of noise.

23

Figure 1-5. Sensitivity curve showing gravitational wave sources in the LISA frequency range compared with its sensitivity for a three arm configuration

The characteristic strain referenced on the y- axis in Figure 1-5 refers to the ratio

of the change in length of the interferometer arms and its original length. The

performance of LISA will be limited by acceleration noise demonstrated by LPF below 3

mHz and limited by interferometric noise above this frequency [16].

1.3 Gravitational Reference Sensor

The Gravitational Reference Sensor (GRS) is comprised of the test mass,

electrode housing, and other associated components as shown in Figure 1-6. The

electrode housing completely surrounds the free floating TM and protects it from

external forces produced by the spacecraft or the space environment. The host

spacecraft uses a drag free system to maintain the position of the TM by using sensors

24

that constantly determine the position of the freely floating TM with respect to the

housing. Information about the position of the TM is sent to a control system which then

commands the spacecraft to reposition itself in such a way that the TM is always

centered within the housing. The spacecraft therefore follows the orbit of the TM. Since

the actuation is not done directly on the TM, the TM avoids any noise associated with

the actuation itself, any residual acceleration noise of the TM will therefore be due to

local forces related to the spacecraft and external forces that are not already absorbed

by the spacecraft [31].

Figure 1-6. Flight-like GRS

1.4 Charge Control on LISA Test Masses

One possible substantial source of acceleration noise for the LISA GRS is

charge build up on the TMs. Charge increases electrostatic stiffness and interacts with

stray electric fields to induce additional force noise. Test masses in LISA must float

freely and the system of discharging must not involve any form of contact therefore

charge build up has to be controlled with UV light using the photoelectric effect. One

way to shine UV light on the test masses is through the use of fiber optic cables. It can

25

be done at DC, which involves illuminating either the gold coated TMs or electrode

housing surfaces to generate a net flow of electrons in the desired direction. This was

first demonstrated on the Gravity probe B mission [7]. It can also be done at AC, where

the UV light is pulsed and synchronized with the 100 KHz AC voltage already present in

the inertial sensor. The UV light would then be switched on only when the voltages

present in the sensor support the flow of electrons in the desired direction and suppress

the flow in the unwanted direction. When the energy of the absorbed light is equal to the

material work function, photoemission occurs for those electrons occupying the highest

energy level.

UV photons require energy above the work function of Au to liberate electrons.

The minimum required illuminating wavelength for a pure Au surface with work function

5.1 eV is ~243 nm. However, contamination generally leads to a lowering of the work

function of Au and allows higher wavelengths to be used [6, 7]. If no bias voltages are

applied to the electrodes surrounding the TM, the illumination of the TM should cause

electron flow from the TM to the housing. However a large fraction of the light will be

reflected to the housing which gives rise to unwanted electron flow from the electrode

housing to the TM. If on the other hand, the housing is illuminated, electrons would flow

from the housing to the TM, light is reflected to the TM and gives rise to unwanted

electron flow from TM to electrode housing. A positive test mass discharge rate is

obtained if the electron flow from the TM to the housing is greater than the electron flow

from the housing to the TM.

1.5 Summary of Chapters

Surface properties as well as preparation and handling that could affect the

Quantum Yields (QY) of Au surfaces intended for use in LISA are addressed in this

26

work. A demonstration of UV LED charge control at AC on a LISA test bed such as the

torsion pendulum described in chapter four is a big step forward in advancing a key part

of one of the technologies required for LISA. AC Charge control was not demonstrated

on LPF. An analytical model that explains the behavior of the pendulum when charge

control is being demonstrated is also important and has been developed.

The characteristics of the UV LEDs used in the QY and pendulum charge control

measurements were examined as detailed in Chapter two. A spectrum analysis was

carried out on both fiber coupled TO18 and non-fiber coupled TO39 UV LEDs from

Sensor Electronic Technology (SETi). Measurements of optical power were also made.

A method for mechanically fiber coupling TO39 UV LEDs was discussed as well. A

driving electronics board was designed and developed to enable pulse width modulation

of the TO39 UV LEDs. This was subsequently used to demonstrate AC charge control

on the pendulum.

Chapter three is dedicated to Investigating Quantum Yield as a function of

several parameters that could affect charge control. A simple analysis of the resulting

QY after multiple reflections showed that the QY of the illuminated surface needs to be

within a factor determined by the reflectivities, R, of both surfaces if they have a

common reflectivity or just the reflectivity, R2, of the surface adjacent to the illuminated

one if their reflectivities differ. A typical Au sample examined for surface composition

revealed a hydrocarbon with oxygen functionalities to be present. No attempt was made

to rid the samples of hydrocarbons, but a bake-out was done to eliminate the effect of

probable water adsorption. After bake-out, repeated measurements on individual

27

samples showed that variations in QY went from a factor of 10 to consistently less than

a factor of 2. A QY dependence on pressure was also shown to be possibility.

In Chapter four, the UF Torsion pendulum is described including its capabilities

for capacitively and interferometrically reading out the position and orientation of the

TMs within the simplified GRS. The acceleration noise performance of the pendulum is

also presented and compared with LISA requirements. An analytical charge control

model developed by representing the relevant surfaces of the GRS as parallel plate

capacitors allowed the distribution of normal energies of the photoelectrons involved in

electron exchange between the plates to be modelled as a function of bias voltages on

the electrodes. Thus an expression for the total electron flow rate for all interfaces was

found. The model adequately explained the voltage due to charge on the test mass

when controlled using DC and AC schemes. One major finding is that the reflectivity of

the gold surfaces allow AC charge control to be performed on any of the three existing

UV injection ports. Another finding is that the TM voltage due to charge can be kept

close to zero as long as the phase of the UV light is set appropriately rather than the

completely “in phase” and “out of phase” configurations usually proposed.

Chapter five discusses how the results obtained impact the LISA design and

operation. Appendix A gives the details the distribution of electron energies as a

function of applied bias voltage. Appendix B completely describes how solutions to

photoelectron flux equations were obtained and Appendix C explains how the charge

measurement equations used on the pendulum are obtained.

28

1.6 Contributions

Finding a method that will make the Quantum Yields of Au samples used in LISA

more uniform and reproducible as well as examining environmental factors that affect

QY was one of the major goals I set out to achieve. With Dr. John Conklin’s supervision,

I designed and implemented a system that enabled Au samples to be set up in a

vacuum chamber in a way that allowed long term QY measurements as a function of

temperature, pressure, and different illuminating UV wavelengths to be made. I also

processed the data from these measurements and analyzed the results as presented in

this dissertation.

Another goal was to demonstrate UV LED charge control on a LISA test bed

such as the UF Torsion pendulum. This was a team effort led by an advisory team

made up of Dr. John Conklin (University of Florida), Dr. Giacomo Ciani (University of

Padua), Dr. Guido Mueller (University of Florida) and Dr. Peter Wass (University of

Florida). Other members of the research team involved in the charge control effort apart

from myself include; Stephen Apple (University of Florida), Andrew Chilton (University of

Florida), Paul Serra (Massachusetts Institute of Technology), Samantha Parry

(University of Florida), Nicholas Turreta (University of Padua) and Henri Inchauspe

(Post Doc. University of Florida).

Paul Serra and I worked together on mechanically fiber coupling 240 nm and 250

nm TO39 UV LEDs for use in Quantum Yield measurements and charge control

experiments on the pendulum. Paul came up with the schematic and design of the

driver board used to synchronize the UV LED with the 100 KHz signal in the pendulum

for AC charge control, I implemented the circuit design for this driver board in Altium

software and sent it to Sierra Circuits to be printed. I also populated the required

29

components on to the Printed Circuit Board (PCB) and incorporated the mechanically

fiber coupled 240 nm UV LED with the driving board in a box to make a complete

charge control unit. Testing the functionalities of the board and fixing major problems

was mostly done by Paul and I. Samantha Parry later worked with Paul to build an

external voltage follower needed to scale the injected voltage signal as needed and

helped with further testing of the board itself.

In addition to implementing an interferometer in the pendulum, Andrew Chilton

designed and implemented the electronics used in data acquisition for capacitive and

interferometric readout on the pendulum. Stephen Apple and I set up and made charge

control measurements at DC and AC on the pendulum. Stephen Apple analyzed the

data afterwards and produced several useful post processed data sets. I worked with

Nicholas Turetta on developing an initial version of the analytical charge control model

which he implemented in Mathematica. I later worked with Henri Inchauspe to

implement a modified and more robust version of the analytical model in MATLAB. I

focused on developing, understanding and implementing the analytical version of the

model as presented in this dissertation but Henri implemented independent versions of

same.

30

CHAPTER 2 UV LEDS FOR LISA TEST MASS CHARGE CONTROL

2.1 Hg Lamps vs. UV LEDs

LISA Pathfinder discharge system exploits the photoelectric effect using UV light

produced by Hg lamps. A proposed discharge system for LISA could follow the same

principle, but replace Hg lamps with UV LEDs which produce light at wavelengths as

low as 240 nm. Their lower mass, better power efficiency and small size make them an

ideal replacement for Hg lamps. Gold samples that are without contamination will not be

discharged of electrons by mercury lamps producing light at 254 nm because the use of

the lamps rely on several unpredictable altered properties of the contaminated samples,

a lowering of the work function being one. Attempts to reduce surface contamination

and purify gold surfaces are therefore not favorable when Hg lamps are intended for

use in discharge. When the spectra of TO18 UV LEDs from SETi were examined, the

240 nm and 250 nm wavelengths peaked at approximately 239 nm (closer to the work

function of pure gold) and 254 nm respectively as shown in Figure 2-1.

Figure 2-1.Left: fiber coupled TO18 UV LEDs from SETi, Right: Intensity spectrum of 240 and 250 nm UV LEDs compared with the work function of Au and the Hg lamp discharge wavelength

31

The TO18 PIV characteristics in Figure 2-2 were found by driving the UV LEDS

with an ILX Lightwave LDX 3200 precision current source and measuring the optical

power with a Thorlabs PM100D power meter with a S120VC detector head.

Figure 2-2. Left: IV curve for TO18 UV LED, Right: PI curve for TO18 UV LED

2.2 UV LED Testing

Further specifications for the TO18 package, indicate that operating the UV LEDs

at 10 ˚C above their maximum operating temperature of 30 ˚C significantly reduces the

number of operating hours [16]. The commercially fiber coupled TO18 package UV

LEDs also failed launch shock vibration tests at Stanford / NASA Ames. It was therefore

decided that a custom, fiber coupler with active thermal control was needed. Two new

non fiber coupled 240 nm UV LEDs from SETi were tested as shown in Figure 2-3; the

TO39 Ball Lens (BL) and the TO39 Hemispherical Lens (HL). Their output optical

powers were found to be ~295 μW and ~200 μW respectively at a maximum current of

24 mA.

32

Figure 2-3. Left: IV curve for 240 nm TO39 BL and HS, Right: PI curve for 240 nm TO39 BL and HS

Figure 2-4. Left: 240 nm TO39 BL UV LEDs, Right: 250 nm TO39 BL UV LEDs

Fiber coupling a TO39 UV LED in the lab as further described in section 2.2.1,

involves collimating the beam with a fused silica bi-convex lens, placing it against a 600

µm core fiber optic cable which has already been glued to a fused silica ferrule, and

mechanically securing the set-up as shown in Figure 2-5.

A choice of the TO39 BL was made for the proposed heat dissipation

management design in Figure 2-6 because the resulting coupling efficiency for the BL

was ~7 % while the HS resulted in a coupling efficiency of ~3%. Also, lifetime tests

33

already carried out on TO39 UV LEDs resulted in > 30000 hours in vacuum and >

12000 hours in Nitrogen [5].

Figure 2-5. Output optical power of TO39 UV LED after being mechanically fiber coupled

2.2.1 UV LED Fiber Coupling and Electronics Driver Board for Charge Control

A UV LED fiber coupler with built-in temperature control was developed for

future space applications at the University of Florida. The design of the fiber coupler as

depicted in Figure 2-6 shows how light from the TO39 UV LED is coupled to the 600 µm

core of a fiber optic cable (FOC) glued inside a fused silica ferrule by a UV curable low

outgassing epoxy. The coupling of the UV light is done by placing a 10 mm focal length

fused silica bi-convex lens between the UV LED and the FOC/ferrule combination. A

mount made out of copper, Aluminum and polymer material is used to hold the unit in

place. The copper holder securing the UV LED before the lens will eventually

incorporate a Thermo-Electric Cooler (TEC) driven by a set of electronics [15].

34

Figure 2-6. Heat dissipation management design

Figure 2-7. UV LED driver board assembled with the UV LED inside a box

In the normal DC operation of the UV LED, a feedback loop on the driving

electronics board depicted in Figure 2-7 regulates any input signal between 0 - 3 V to

output a 0 - 3 V signal that is proportional to a current between 0 and 30 mA. When the

operation of the board goes from DC operation to pulse width modulation (PWM) of the

UV LED, parameters such as phase, amplitude voltage and duty cycle can be adjusted

35

by using variable resistors. Efforts will be made to space qualify the final version of the

driver board which will incorporate digital control electronics. Thermal vibration and

shock tests will be performed to verify its compatibility with the space environment.

2.2.2 Proposed Heat Dissipation Management

Heat from the TEC due to contact with the base of the UV LED will conduct

through the copper piece to the body of the assembly to a heat sink such as the

Aluminum box containing the unit in Figure 2-7. The TEC will be driven by an ADN8831

controller which incorporates a proportional integral differential (PID) feedback

mechanism that will stabilize the temperature of the unit by feeding back the sensed

temperature to complete a “closed thermal control loop of the TEC” [24].

2.3 Performance of UV LED Driver Board

Testing of the driver board included validating the power output of the UV LED

when driven at inputs of 0 - 3 V (corresponding to driving currents of 0- 30 mA) and duty

cycles of 5 % to 15 %. Charge control experiments on the torsion pendulum were

mostly carried out by setting the UV LED at a 5 % duty cycle with respect to the

injection because this value is small enough for a constant average injection voltage to

be assumed during the UV light pulse. Figure 2-8 shows the average UV power output

while driving the UV LED at 5-20 mA, increasing almost linearly and is stable with

standard deviations mostly below 0.1% of the average power output at each voltage.

Varying the duty cycle while driving the UV LED at 10 mA gives the results shown in

Figure 2-9. The power output here is also stable with a standard deviation of less than

0.1 % of the output for each duty cycle.

36

Figure 2-8. Average power output of UV LED driver board for a 5 – 20 mA current setting input and a constant 5 % duty cycle

Figure 2-9. Average power output of UV LED driver board for various duty cycle settings

37

CHAPTER 3 QUANTUM YIELD AND REFLECTIVITY OF LISA TEST MASSES

3.1 Motivation for Measuring QY and Reflectivity

One of the critical properties governing the performance of a charge

management system is the apparent Quantum Yield (QY). The QY is calculated as the

number of photoelectrons emitted from the gold surface per incident UV photon. It is

important to know the amount of UV light absorbed by opposing surfaces under

illumination since in the LISA Pathfinder GRS design; both the TM and the electrode

housing are gold coated. When UV light illuminates the TM directly, some of the light

reflects back and is absorbed by the housing. This can create photoelectrons that flow

in opposition to the intended direction. Large QY differences in the surfaces involved in

charge control may also result in electron flow in only one direction irrespective of which

one is illuminated. Therefore the relationship between the QYs and reflectivities of

surfaces involved in charge control should be understood. Studies show that the TM

absorbs about 70% of the total light when it is illuminated and about 20% is absorbed by

the housing. When illuminating the housing, around 25% is absorbed by it and about

15% by the TM [Hollington, Daniel. 2011], the remaining percentage is lost in crevices

and gaps in the electrode housing that are not involved in the charge control process.

3.2 Reflectivity Analysis for Two Infinite Parallel Plates

Adjacent surfaces intended for use in charge control should ideally have identical

Quantum yields so that when one of the surfaces is illuminated, all the electrons will

make the transition in the desired direction. However reflections make this nearly

impossible. Maximum deviations from the ideal that still allow for effective charge

control should follow the approximate rules derived in the following two cases;

38

The number of electrons 𝑁𝑒 ejected by a surface with incident UV light photons

𝑁𝑣 can be represented as;

𝑁𝑒 = 𝑁𝑣𝑄𝑌 (3-1)

The surfaces in Figure 3-1 with quantum yields QY1 and QY2 and equal

reflectivities, R with UV light directed at surface 1, can have the total number of

photoelectrons due to multiple reflections represented as follows;

Figure 3-1. Reflections between two surfaces with different QYs and similar reflectivities

Assuming N reflections between surfaces 1 and 2, the net number of electrons

flowing from surface 1 to 2 is,

𝑁𝑒 = 𝑁𝑣𝑄𝑌1 + 𝑁𝑣𝑄𝑌1 𝑅2 + 𝑁𝑣𝑄𝑌1 𝑅

4 + ⋯ − 𝑁𝑣𝑄𝑌2 𝑅 − 𝑁𝑣𝑄𝑌2 𝑅3 − 𝑁𝑣𝑄𝑌2 𝑅

5 − ⋯

(3-2)

Combining the terms gives,

𝑁𝑒 = 𝑁𝑣 ∑ (𝑄𝑌1

𝑁𝑛=0 𝑅2𝑛 − 𝑄𝑌2 𝑅

2𝑛+1 ) (3-3)

𝑁𝑒 = 𝑁𝑣 ∑ 𝑅2𝑛𝑁

𝑛=0 (𝑄𝑌1 − 𝑄𝑌2 𝑅) (3-4)

For an infinite number of reflections, N ∞,

39

∑ 𝑅2𝑛𝑁𝑛=0 =

1

1−𝑅2 (3-5)

And therefore, the net number of electrons becomes,

𝑁𝑒 = 𝑁𝑣1

1−𝑅2(𝑄𝑌1 − 𝑄𝑌2 𝑅) (3-6)

If 𝑁𝑒 > 0, then,

𝑅 <𝑄𝑌1

𝑄𝑌2

< 𝑅 (3-7)

Therefore, the net flow of electrons away from the illuminated surface will be

positive if the QY of that surface is greater than R.QY of the opposing surface. If a 36%

reflectivity is assumed based on previous work done on Au surfaces [8] then Equation

3-7 shows that for two surfaces involved in charge control with different QYs and similar

reflectivities, the net flow of electrons will be away from the illuminated surface if the QY

of that surface is greater than the QY of the opposing surface by a factor of 0.36 or

more.

If the reflectivities of the two surfaces are different, say 𝑅1 and 𝑅2 as in Figure 3-

2, the total number of electrons flowing away from surface 1 is given by,

𝑁𝑒 = 𝑄𝑌1𝑁𝑣 + 𝑄𝑌1𝑁𝑣𝑅2𝑅1 + 𝑄𝑌1𝑁𝑣𝑅2𝑅1 + ⋯

−𝑄𝑌2𝑁𝑣𝑅2 − 𝑄𝑌2𝑁𝑣𝑅22𝑅1 − 𝑄𝑌2𝑁𝑣𝑅2

3𝑅12 − ⋯ (3-8)

Combining terms gives,

40

Figure 3-2. Reflections between two surfaces with different QYs and different reflectivities

= 𝑁𝑣(𝑄𝑌1(1 + 𝑅2𝑅1 + 𝑅22𝑅1

2 + ⋯ ) − 𝑄𝑌2(𝑅2 + 𝑅22𝑅1 + 𝑅2

3𝑅12 + ⋯ )) (3-9)

And

= 𝑁𝑣(𝑄𝑌1(∑ (𝑅2𝑅1)𝑛) − 𝑄𝑌2𝑅2(∑ (𝑅2𝑅1)𝑛𝑁𝑛=0

𝑁𝑛=0 )) (3-10)

If N ∞, then the following holds

∑ (𝑅2𝑅1)𝑛 = 1

1−𝑅2𝑅1 𝑁

𝑛=0 (3-11)

= 𝑁𝑣(𝑄𝑌1(1

1−𝑅2𝑅1) − 𝑄𝑌1𝑅2(

1

1−𝑅2𝑅1)) (3-12)

= 𝑁𝑣

1−𝑅2𝑅1(𝑄𝑌1 − 𝑄𝑌2𝑅2) (3-13)

For 𝑁𝑒 > 0

𝑅2 <𝑄𝑌1

𝑄𝑌2< 𝑅1 (3-14)

So the QY of the illuminated surface must be greater than the QY of the opposing one

by a factor determined by the reflectivity of that opposing surface.

In reality, the number of reflections N, between GRS surfaces is not infinite but

the above derivations follow a reasonable “rule of thumb”. Actual required QY ratio

depends on detailed light distribution over a more complex geometry.

41

3.3 QY Experimental Set up and Apparatus Description

The quantum yields of several Au samples have been quantified by isolating a

2 in × 2 in gold sample inside a hollow 3.5 in diameter sphere using Ultem holders

which have a resistivity of 1017 Ωm [5]. In the set-up in Figure 3-3, the sphere is biased

positively (+9 V) and the sample negatively (−9 V), this was done by using 9 V batteries

to reduce ground loops. An ultra-high vacuum UV fiber optic cable with a 600 μm core is

used to direct the light from the UV LED to the sample at a zero degree incident angle.

The UV LED current is then varied over a range of 10 mA-24 mA, using an ILX

Lightwave LDX-3200 precision current source. This range of current corresponds to 6

μW-20 μW of optical power with only 0.6 μW-2 μW directly incident on the Au sample in

the chamber after accounting for losses through fiber couplings. At a maximum current

draw of 24 mA, both the 240 nm and 250 nm UV LEDs consume roughly 180 mW of

electrical power. The resulting photocurrent is measured using a Keithley 6485

Picoammeter. This is then converted to number of photoelectrons and divided by the

number of incident illuminating UV photons [16]. Even though the Aluminum sphere

absorbs some of the UV light reflected by the gold sample, any electrons ejected from

its surface is trapped by the large 18 V retarding potential barrier and does not factor

into the Quantum Yield calculations. The quantum yield measurement results presented

in this work were made at pressures of 10−6 Torr to 10−8 Torr by using both vacuum

chambers shown in Figure 3-3.

A local bake-out of the sample can be carried out by attaching a 28 V, 5 W

polyimide film strip heater to the back of the Au sample. The heater is connected to an

LM2575T regulator which provides a differential 5 V input to an LT1006 operational

42

amplifier and an IRF3708 MOSFET for switching the output voltage connected to a

PT1000 sensor also attached to the sample on and off. A standard data sheet gives the

sensor temperatures and corresponding resistance values. These resistances are used

to determine the voltages to be set by an incorporated potentiometer.

Figure 3-3. QY measurement apparatus set up in large vacuum at ~3 × 10−6 Torr, QY apparatus was subsequently set up in the small vacuum chamber with a leak valve for pressure adjustments

3.3.1 QY Dependence on Energy of Emitted UV Light

The quantum yields of most metals have a linear dependence on the wavelength

of the incident UV light with lower wavelengths resulting in higher quantum yields and

vice versa [19]. The energy of the emitted photoelectrons has a value between 0 eV and

43

a maximum energy given by (hν − ɸ) eV [17]. The maximum energy is related to the

quantum yield through the following relationship.

𝑄𝑌 ∝ (ℎ𝜈 − ɸ)2 (3-15)

The QY experiments carried out in this work are done at 240 nm and 250 nm. A

rough estimate of the validity of the results obtained can be found by considering two

different wavelength UV LEDs and representing Equation 3-15 as,

𝑄𝑌𝑙𝑤 = 𝛽 (ℎ𝑐

𝜆𝑙𝑤− ɸ𝐴𝑢)2 (3-16)

𝑄𝑌ℎ𝑤 = 𝛽 (ℎ𝑐

𝜆ℎ𝑤− ɸ𝐴𝑢)2 (3-17)

Here, 𝑄𝑌𝑙𝑤 and 𝑄𝑌ℎ𝑤 represent the respective QY values obtained at the lower

and higher wavelengths while λlw and λhw are the corresponding wavelengths in nm, h is

Planck’s constant (4.1357 × 10−15 eV s) β is a constant, c is the speed of light (3 × 108

m/s) and ɸAu is the work function of the Au sample under experiment. Dividing Equation

3-16 by Equation 3-17 results in,

ɸ𝐴𝑢 = − ℎ𝑐

(1−√𝑟)(

√𝑟

𝜆ℎ𝑤−

1

𝜆𝑙𝑤) (3-18)

When more than one UV wavelength is used in the QY measurements, a rough estimate

of the work functions of the measured Au samples can be found from Equation 3-18.

Previous work function measurements carried out on several Au samples at the

University of Modena have values between 3.6 eV to 5.1 eV with an average of 4.3 ±

0.4 eV [8]. If the results from Equation 3-18 fall within this range, then the QY results

obtained would seem reasonable.

44

3.3.2 QY Measurements and Wavelength

One of the factors influencing the measured QYs of Au surfaces include the

energy of the illuminating photons from the UV light. The work here focuses on two

different UV LED wavelengths, the 240 nm UV LED with a corresponding energy of

~ 5.17 eV and the 250 nm UV LED corresponding to an energy of ~4.96 eV. Regardless

of surface preparation and handling, the closer the work function of the surface is to the

energy of the illuminating photons, the more likely it is that photoelectrons will be ejected

from that surface.

The QYs of several random Au samples have been quantified as shown in Figure

3-4. Samples 1 (A, B, C, D) were coated in March 2013 with a gold layer 200 nm thick

and samples 2 (A, B) with a gold layer 500 nm thick were coated in September 2013.

The letter P indicates a polished surface and the letter U, an unpolished surface so that,

1AP is the measurement made on a polished surface coated in the first batch of samples

and 2BU is that made on an unpolished surface coated with the second batch. The

measurements were made in 2014. The dates are as indicated. The vacuum chamber

was vented back to atmospheric pressure in between measurements. As expected and

shown, the 240 nm UV LEDs result in a higher QY than the 250 nm ones. Both UV LEDs

are similar in terms of power consumption and cost.

The QY measurements vary by as much as a factor of 20 across the different

samples with individual samples varying by factors of 1.2 to 10. An example is sample

1CP which produces QYs varying by a factor of ~2 for four successive measurements

made within a period of three weeks without breaking vacuum. There is an overall lack of

repeatability in the measurements which is believed to be due in part to atmospheric

45

contaminants which adsorb on the sample surface while in storage and from the walls of

the vacuum chamber during the experiment.

Figure 3-4. QY of Au samples at 240 nm > QY at 250 nm

The effect of water adsorption on the sample surface is an increase in the work

function [21]. Previous work has shown that unlike water, carbon compounds cannot be

gotten rid of by baking out the sample, but argon sputtering successfully removed carbon

compounds and led to an increase in work function [22] meaning that the presence of

carbon compounds may have led to a reduction of same.

3.3.3 QY Measurements vs. Time

The measured QYs of some of the Au samples in Figure 3-4 appear to be

inconsistent with no indication of what the actual values could be. It might be possible to

obtain more information about this behavior with longer term measurements. For this

purpose, sample 1DP was measured, using a UV wavelength of 240 nm under vacuum

46

for two weeks. The vacuum chamber was briefly vented up to atmosphere once during

this time period in order to see what the effect of possible atmospheric compounds

interacting with the sample surface could be. Apart from a slight decrease in the QY after

the vacuum chamber was pumped down again, the QY continued to increase until it was

up to a factor of 2 over 300 hours as shown in Figure 3-5. This suggests that even

though all samples were cleaned to remove surface impurities just before testing, they

still come in contact with contaminants such as water and hydrocarbons adsorbed

through contact with the atmosphere before being set up in vacuum.

Figure 3-5. Successive QY measurements with sample 1DP held at 10−5 Torr using a UV wavelength of 240 nm

3.3.4 QY After a Bake-out

One way to reduce variations in QY may be to get rid of contaminants on the

sample surface by baking it out in vacuum [8]. A bake-out of sample 2BP was carried out

in vacuum at 130 ˚C over a period of 550 days. The QY measurements, using a

47

wavelength of 240 nm are shown in Figure 3-6. During this process, just before the bake-

out was started on the sample, a QY measurement was made. Another was made

immediately after the sample reached 130 ˚C and others while the sample was being

baked further. Within the first few hours, an increase in the measured QY, from ~9 ×

10−7 to ~2 × 10−5 was observed indicating that impurities evaporating from the sample

surface probably lowered the work function. The QY eventually stabilized at ~ 7 × 10−6

(previously measured as ~ 4 × 10−7 in Figure 3-4) for three repeated cycles of

measurements made after the heater was turned off and the sample allowed to cool

down to room temperature without venting the chamber, indicated by the points in green

(these are the only points considered in the ongoing discussion). These QY

measurements appear to be fairly uniform and are within a factor of 1.3 of one another

for the 0° UV incidence angle after three cycles of repeated measurements on the same

sample.

The UF torsion pendulum is a test bed for LISA GRS technology which will be

discussed in chapter 4. In the current version of the pendulum’s simplified GRS, UV light

incident on the TM and EH are each at a 45 ° incidence angle. This prompted the need

to make QY measurements with the UV LED inclined at 45° to sample 2BP. The

resulting QYs lie within a factor of 1.08 for repeated measurements. These are slightly

lower than those made at 0 °by about a factor of 1.2. At 0°, more of the UV light is likely

absorbed by the sample surface than at 45° which could explain the slightly higher

quantum yield. From previous work done, the amount of reflected light for 0° and 45°

are approximately 36 % and 37 % respectively for unpolarized UV light [8,23]. This is

illustrated in Figure 3-7.

48

Figure 3-6. Measured QY on Au sample 2BP with bake-out at 130˚C and 240 nm

Figure 3-7. Fraction of light reflected as a function of angle of incidence (in degrees) for 254 nm wavelength showing the two polarization components Rp and Rs

comparing results described by Daniel Hollington (Dissertation 2011) and Johnson and Christy (1972).

Measurement before bake-out with UV light at 45 degrees Measurement during bake-out with UV at 45 degrees

49

The green points after the heater is turned off and the sample has been allowed

to cool are important because the LISA GRS will be baked out before launch to provide

more uniform quantum yields required for effective charge control. Points in yellow are

those taken before the bake-out measurements at 45˚.

3.3.5 Sample Preparation, Cleaning and Storage

The samples discussed so far were generally hand polished and stored in

designated cabinets in air at room temperature with no special cleaning procedure.

However, care was taken to make sure that protective gloves were worn when handling

them. In an effort to investigate if the handling of the samples had any significant effects

on the QY, a dedicated cleaning procedure for Au samples was obtained from Imperial

College London (ICL). The research group at ICL was responsible for the charge

management system for LISA Pathfinder. The procedure is outlined as follows,

Step 1: Ten minutes ultrasound immersed in acetone

Step 2: Rinse with de-ionized water

Step 3: Ten minutes ultrasound immersed in ethanol

Step 4: Rinse with de-ionized water

Step 5: Ten minutes ultrasound immersed in propan-2-ol

Step 6: Warm propane-2-ol containing sample in warm water bath

50

Step 7: Remove sample slowly allowing alcohol to drain and evaporate as the sample is

lifted

Step 8: Ensure that the surface has no tide marks

Step 9: Remove any remaining droplets with clean dry Nitrogen

Step 10: Attach connectors, mount in vacuum system and begin pumping down

immediately

The above cleaning steps were applied to two separate Au samples, 1CP and

1AP, before doing a bake-out at 130 °C. Figure 3-8 shows the QY of sample 1CP at 240

nm stabilizing at ~ 8 × 10−6 (average of green points) over 700 hours, this a factor of 6

increase over the average of ~1.3 × 10−6 that was obtained for the same sample without

a bake-out shown in Figure 3-4 using 240 nm UV LEDs. The overall result does remains

fairly consistent (in the 10−6 range) with those obtained from other samples from this

batch after a bake-out without any special consideration for cleaning and handling. The

same procedure applied to sample 1AP in Figure 3-9 follows the same pattern as 1CP

with additional measurements made simultaneously at 250 nm.

The QY for the 240 nm wavelength averages at 1.2 × 10−5 after baking out

(green points); this is a factor of 1.5 above the 0.8 × 10−5 average obtained from Figure

3-4 with no bake-out. The measurements at 250 nm resulted in a lower value of 0.23 ×

10−5, a factor of ~2 increase over the values obtained in Figure 3-4 at 250 nm.

51

Figure 3-8. QY with detailed cleaning procedure and bake-out at 130°C using 240 nm UV LEDs for sample 1CP

Figure 3-9. QY with detailed cleaning procedure and bake-out at 130°C with UV wavelengths of 240 nm vs. 250 nm for sample 1AP

QY at 240 nm with 130˚C bake-out

QY at 250 nm with 130˚C bake-out

Measurement before bake-out Measurement after turning heater off Measurement after vacuum is vented and pumped down again

52

3.3.6 Evaluating the QYs of Commercially Polished Au Surfaces

Apart from atmospheric contaminants which could be reduced by baking out the

sample, another likely reason for the variation in measured QY is that the samples were

not prepared in a consistent manner. All the Au samples discussed so far were hand

polished Aluminum substrates, gold-coated by Teer coatings in the UK and tested with

the fiber coupled TO18 UV LEDs described in section 2.1.

The new samples called 4AP, 4BP, 4CP, 4DP were Aluminum substrates

commercially polished in August 2017 by Cabot Microelectronics. The polishing was

done by diamond fly cutting to a specification of less than 10 µm for flatness and 12-16

nm for surface roughness before being sent off to Teer Coatings to be gold coated.

These samples were not cleaned in any way before QY measurements. They were

simply stored in clear all-glass petri dishes inside a shelf in the lab after they were coated

and received from Teer Coatings UK. The samples were evaluated with TO39 UV LEDs

fiber coupled as described in section 2.2. These 240 nm and 250 nm TO39 UV LEDs

peaked at 247 nm and 255 nm respectively.

As shown in Figure 3-10, three cycles of measurements were made on sample

4AP at a pressure of ~2 × 10−6 Torr over 500 hours with a 130 ˚C bake-out. As with

previous bake-out measurements, the blue points are the measurements made after the

vacuum chamber is pumped down before the bake-out is started. The red points

represent the measured QYs while the sample is being held at 130˚C. The points in

green are measurements made after the heater is switched off and the sample is allowed

to cool down to room temperature. The cyan points represent measurements made

immediately after the vacuum is pumped down again after venting. The pressure

adjustments are shown in grey. Measurements revealed a fairly consistent QY with

53

values of ~7 × 10−5 after the heater was switched off and the sample was allowed to

cool.

Figure 3-10. QY of Commercially polished sample 4AP measured at 130°C with a 240

nm at ~2x10−6 Torr

Only one sample can be set up in the chamber at a time and prolonged

measurements such as the one shown in Figure 3-10 could take several weeks.

Previous bake out results show that the average of the green points do not change

significantly with repeated measurements. This is why an average of three cycles was

chosen for the measurements on the commercially prepared samples.

3.3.7 Investigating QY Dependence on Pressure

The UF torsion pendulum which will be discussed in Chapter 4 operates at

~10−6 Torr but the LISA GRS will operate around 10−8 Torr. This motivates the need to

54

investigate possible QY dependence on pressure. The current vacuum chamber in

Figure 3-3 uses O-rings which do not provide as good of a vacuum seal as copper

gaskets. The lowest vacuum pressure obtained with the O-ring seals averaged at

~ 3 × 10−6 Torr. A set up capable of reaching pressures as low as ~2 × 10−8 Torr range

was achieved by designing a smaller vacuum chamber with all feedthroughs sealed with

copper gaskets. The smaller vacuum chamber was also baked out to help get rid of

substances which might out gas and contribute to a lowering of overall vacuum quality.

Variations in vacuum pressure in the new vacuum chamber were obtained with a

variable leak valve from Agilent Technologies, which offers leak rates as small as

1 × 10−10 Torr-liters per second and almost precisely controls the size of the leak.

Samples 4AP, 4BP, 4CP and 4DP were investigated at three different pressures and a

130 °C bake-out temperature as shown in Figures 3-11, 3-12, 3-13 and 3-14. The first

noticeable detail is that 4AP has lower QY values than the other three samples;

averaging between 4 − 7 × 10−5 at 240 nm and 2 − 4 × 10−5 at 250 nm shown in

Figures 3-16 and 3-17 respectively. This may be because the whole chamber along with

this particular sample set up inside, was baked out to temperatures as high as 200°C to

help drive the vacuum chamber pressures into the proposed LISA range. The actual

local bake-out on the sample was done afterwards at 130°C before cooling down to

make QY measurements. It is likely that the surface properties of the sample were

already altered by the 200 ˚C bake-out so that making measurements after this bake-out

at a temperature below this value did not have the same effect on the quantum yields

compared to the other three samples. This is also evident in the standard deviations from

measurement to measurement on this sample. Overall, sample 4AP shows no significant

55

variation with pressure since the standard deviations mostly overlap. The 200° C initial

bake-out does not apply to the other three samples in this discussion.

Figure 3-11. QY of sample 4AP measured between 10-8 and 10-6 Torr

Figure 3-12. QY of sample 4BP measured between 10-8 and 10-6 Torr

56

Figure 3-13. QY of sample 4CP measured between 10-8 and 10-6 Torr

Figure 3-14. QY of sample 4DP measured between 10-8 and 10-6 Torr

Additional measurements of more than 1000 hours were made on sample 4 CP at

10−8 Torr after concluding the third measurement cycle without breaking vacuum. As

shown in Figure 3-15, the measured QYs reduced to a factor of two below what the

average was at 10−6 Torr. This is important because LISA will undergo a long integration

57

process where pressures could rise to values as high as 10−5 Torr after intermittently

breaking vacuum. This pressure will be adjusted to 10−8 Torr after it is released into the

space environment. It is important to take changes as a result of expected pressure

variations into account.

Figure 3-15. Long term QY measurements of sample 4CP at 10-8 Torr

All the measured QYs represented by the green points in Figures 3-11 to Figure

3-14 were plotted as shown in Figure 3-16 and Figure 3-17. Samples 4BP and 4CP are

directly comparable in how they were handled because at the time of measurement, the

pressure in the chamber easily reached the 10−8 Torr range and could be increased by

factors of ten when needed. However, this was not the case for 4DP where pressures in

the lower regions of 10−8 Torr could not be easily accessed probably due to a leak

somewhere in the vacuum system.

The QYs of samples 4BP and 4CP do not appear to have a significant pressure

dependence at 10−8 and 10−7 Torr since the QYs for these samples fall within similar

58

ranges at these two pressures. At 10−6 Torr however, the mean QYs for both samples

reduce by as much as a factor of 3. This could be because; for one, at 10−6 Torr, water is

present in a much higher quantity on the sample surface than at the starting pressure of

10−8 Torr. This most likely led to an increase in the work functions and resulted in lower

QYs. Sample 4DP followed a similar pattern to 4BP and 4CP at pressures of 10−8 and

10−7 Torr. There was no meaningful QY change at 10−6 Torr.

Figure 3-16. Results of QY as a function of pressure at 240 nm

Figure 3-17. Results of QY as a function of pressure at 250 nm

59

3.5 Summary of QY Measurements

A summary of all QY measurements made so far is provided in Table 3-1. Some

of the information in the table includes the approximate date the samples were coated,

the way they were processed and the UV wavelengths used in the measurements.

Table 3-1 Quantum Yield Measurements from Au samples coated from March 2013

through August 2017, refer to Figures 3-4 through 3-14

Parameters Average QY at 240 nm

Average QY at 250 nm

Sample#: 1AP Date of coating: March 2013 Processing: Hand polished 8 × 10−6 1.2 × 10−6 Cleaning method: Wiping with Isopropanol Figure 3-4 Figure 3-4 UV light angle with respect to the sample: 0° Temperature: Ambient Pressure: 3E-6 Torr

Sample#: 1BP Date of coating: March 2013 Processing: Hand polished 2.5 × 10−6 1.5 × 10−7 Cleaning method: Wiping with Isopropanol Figure 3-4 Figure 3-4 UV light angle with respect to the sample: 0° Temperature: Ambient Pressure: 3E-6 Torr Sample#: 1CP Date of coating: March 2013 Processing: Hand polished Cleaning method: Wiping with Isopropanol UV light angle with respect to the sample: 0°

Temperature: Ambient Pressure: 3E-6 Torr Sample#: 1DP Date of coating: March 2013 Processing: Hand polished Cleaning method: Wiping with Isopropanol UV light angle with respect to the sample: 0°

Temperature: Ambient Pressure: 3E-6 Torr

1 × 10−6 Figure 3-4

1.2 × 10−5

Figure 3-4

4.6 × 10−7 Figure 3-4

6 × 10−7

Figure 3-4

60

Table 3-1. Continued



Sample#: 2AP Date of coating: September 2013

Processing: Hand polished 9 × 10−6 5 × 10−6 Cleaning method: Wiping with Isopropanol Figure 3-4 Figure 3-4 UV light angle with respect to the sample: 0° Temperature: Ambient Pressure: 3E-6 Torr Sample#: 2BP Date of coating: September 2013

Processing: Hand polished 4 × 10−7 -

Cleaning method: Wiping with Isopropanol Figure 3-4 UV light angle with respect to the sample: 0° Temperature: Ambient Pressure: 3E-6 Torr Sample#: 2BU Date of coating: September 2013 Processing: Unpolished Cleaning method: Wiping with Isopropanol UV light angle with respect to the sample: 0°

Temperature: Ambient Pressure: 3E-6 Torr

1.6 × 10−7

Figure 3-4 8 × 10−8

Figure 3-4

Sample#: 2BP Date of coating: September 2013 Processing: Hand polished Cleaning method: Wiping with Isopropanol UV light angle with respect to the sample: 0°

Temperature: Baked out at 130 °C Pressure: 3E-6 Torr

Stable green points after cooling

7 × 10−6

Figure 3-6

-

Sample#: 2BP Date of coating: September 2013 Processing: Hand polished Cleaning method: Wiping with Isopropanol UV light angle with respect to the sample: 45°


5.5 × 10−6


Figure 3-6

-

61




Sample#: 1CP Date of coating: March 2013 Processing: Hand polished Cleaning method: Procedure from ICL UV light angle with respect to the sample: 0°


Stable green points after

cooling

8 × 10−6

Figure 3-8

-

Sample#: 1AP Date of coating: March 2013 Processing: Hand polished Cleaning method: Procedure from ICL UV light angle with respect to the sample: 0°

Temperature: baked out at 130 °C Pressure: 3E-6 Torr


cooling

1.2 × 10−5 Figure 3-9


cooling

2.3 × 10−6 Figure 3-9

Sample#: 4AP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°

Temperature: Baked out at 130 °C Pressure: 1.5E-6 Torr


cooling

7 × 10−5 Figure 3-10

-




cooling

5.9 × 10−5 Figure 3-11


cooling

3.9 × 10−5 Figure 3-11

Sample#: 4AP Date of coating: August 2017 Processing : Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°



cooling

6.5 × 10−5 Figure 3-11


cooling

3.8 × 10−5 Figure 3-11

62





Temperature: Baked out at 130 °C Pressure: 2E-6 Torr Sample#: 4BP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°


Stable green

points after cooling

6.3 × 10−5 Figure 3-11

Stable green


2.5 × 10−4 Figure 3-12


cooling

3.5 × 10−5 Figure 3-11


cooling

1.3 × 10−4 Figure 3-12

Sample#: 4BP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°


Stable green


2 × 10−4 Figure 3-12


cooling

1 × 10−4 Figure 3-12

Sample#: 4BP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°



8 × 10−5 Figure 3-12


cooling

3.8 × 10−5 Figure 3-12

Sample#: 4CP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°



3.1 × 10−4 Figure 3-13


cooling

1.5 × 10−4 Figure 3-13

63




Sample#: 4CP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°

Temperature: Baked out at 130 °C Pressure: 3E-7 Torr Sample#: 4CP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°


Stable green points

after cooling

3 × 10−4 Figure 3-13

Stable green points

after cooling

2 × 10−4 Figure 3-13


cooling

1.6 × 10−4 Figure 3-13


cooling

7 × 10−5 Figure 3-13

Sample#: 4DP Date of coating: August 2017 Processing: Diamond turned polishing Cleaning method: None UV light angle with respect to the sample: 0°

Temperature: Baked out at 130 °C Pressure: 6E-8Torr

Stable green points

after cooling

2.1 × 10−4 Figure 3-14


cooling

9.2 × 10−5 Figure 3-14



Stable green points

after cooling

2.1 × 10−4 Figure 3-14


cooling

9.6 × 10−5 Figure 3-14



Stable green points

after cooling

2.1 × 10−4 Figure 3-14


cooling

8 × 10−5 Figure 3-14

64

3.6 Alternative Coatings Explored

Gold is the default coating material for the LISA test mass and housing because

of its non-magnetic properties and uniform surface potential which reduces spurious

force noise on the test mass. Gold is reflective at 1064 nm, the wavelength of the laser

interferometer, and is suitable for UV photoemission-based charge control. It is also soft

and prone to sticking and scratching when not properly handled and could complicate

the caging and release process. Carbide coatings on the other hand have been

considered as potential alternatives, therefore the QYs of some alternate carbide

coatings have been explored. Four extra samples each of Au, TiC and SiC were coated

at TEER coatings as shown in Figure 3-18. They were measured at 240 nm UV

wavelength without doing a bake-out. The coatings applied were, Ti (50 nm, 99.5%

purity) followed by Au (500 nm, 99.99% purity), Ti (50nm, 99.5% purity) followed by TiC

(500 nm, 99.5% purity) and Si (50 nm, 99.99% purity) followed by SiC (500 nm, 99.99%

purity).

Figure 3-18. Left to right; Aluminum substrates, hand-polished and coated with Au, TiC and SiC

Figure 3-19 shows the QYs for Au as the highest of the three varying between

~2 × 10−6 and ~1.3 × 10−5. TiC with work function 3.80 eV [9] is the most stable

between ~3.5 × 10−7 and ~6 × 10−7. SiC with work function 4.80 eV [10] results in QY

values from ~2.1 × 10−7 to ~1 × 10−6.

65

Figure 3-19. Results of QY measurements for Au, TiC, and SiC coatings

The reflectivities calculated for TiC and SiC at 255 nm were found to be 15% and

12% respectively [5], meaning that they would absorb sufficient amount of photons and

would be suitable alternative materials for charge control. Since the time of these

measurements LISA Pathfinder successfully demonstrated UV charge control and

caging and release, solidifying the use of Au as the coating choice for LISA. However,

other missions could consider these materials in the future.

3.7 X-ray Photoelectron Spectroscopy Measurements

The prevalence of non-reproducible QY measurements on non-annealed gold

samples motivated the need to determine the surface composition of the gold samples

used in QY measurements and find a process that would make the surface properties

more uniform for consistent QYs across samples.

Au, TiC, SiC

66

X-ray Photoelectron Spectroscopy (XPS) measurements, carried out at the

University of Florida in the Ultrahigh-Vacuum Lab at the department of materials science

and engineering were used to analyze and determine the chemical composition on the

surfaces of two gold samples. Both samples were 0.7 in × 0.6 in steel plates, first coated

with Ti (50 nm, 99.5% purity) for non-magnetism followed by Au (500 nm, 99.99% purity)

by Teer coatings. XPS uses the principle of photoelectric effect which involves the

excitation of electrons by photons. The setup includes a monochromatic X-ray source, a

sample chamber and an electron analyzer, all in ultra-high vacuum [33]. The first Au

sample was cleaned with isopropanol in the same way some regular Au samples were

cleaned before QY measurements. This sample was transferred to XPS vacuum within

one hour. The elements present on the surface of the gold sample are identified in Table

3.2 while Figure 3-20 shows the XPS measured spectrum of the sample.

Table 3-2: XPS measurements for bare Au sample cleaned with isopropanol

Peak Intensity (CPS) Atomic Ratio (%) Sensitivity factor

Au 4f 194340 0.671625695 5.24 O1s 1214 0.030920427 0.711 C1s 4862 0.297453878 0.296 S2p 0 0 0.57

The second Au sample was treated in 1-Dodecanethiol solution for 24 hours. The

molecules of the thiol solution adsorb and form protective, well-arranged, chemically

stable and self-assembled hydrocarbon monolayers on an inert substrate like Au [18].

67

Figure 3-20. The XPS measurements of bare Au cleaned with isopropanol

The layer assembled in this case was reproducible with a thickness of 1.5 - 2.5 nm. The

sample was rinsed with ethanol and dried with N2 before being transferred to the XPS

vacuum within the hour. Figure 3-21 shows the spectrum of the electrons in counts per

second (CPS) plotted against the binding energy of the electrons on the material surface.

Each XPS peak identifies the elements that are present on the surface of the gold

sample which are listed in Table 3-3.

Table 3-3. XPS measurements for Au sample treated with Thiol.

Peak Intensity (CPS) Atomic Ratio (%) Sensitivity factor

Au 4f 66040 0.357304464 5.24 O1s 0 0 0.711 C1s 6490 0.621606648 0.296 S2p 424 0.021088887 0.57

68

Figure 3-21. XPS measurement spectrum of Au after being treated in thiol solution for 24 hours

The results obtained from the XPS measurements are consistent in terms of the

composition of what would be expected for samples prepared in these ways. It was

further determined that the sample cleaned with isopropanol had at least, a 1 nm thick

film of an unknown hydrocarbon with oxygen functionalities that would be unavoidable in

a QY measurement where the sample preparation process involves cleaning with

isopropanol only.

Repeated QY measurements made on a third 2 in × 2 in Au sample prepared with

the self-assembled monolayer gave results between 2.75 × 10−4 and 2.9 × 10−4, a

factor of 1.05 in maximum variation. This is a significant improvement from the samples

69

in Figure 3-4, where repeated measurements on individual samples varied by factors of

1.2 to 10. These measurements are comparable since they were made at the same

pressure but are not conclusive because only one sample with the monolayer was tested

for QY.

3.8 Conclusions

The results obtained in this chapter are summarized here with conclusions and

recommendations useful for the LISA mission.

Baking out the Au test samples at 130 ˚C had the effect of reducing likely

contamination from probable water adsorption on the sample surface and resulted in

more uniform QYs. Before a bake-out, individual samples varied in QY by factors of 1.2

to 10 for repeated measurements at 10−6 Torr and UV wavelengths of 240 nm and 250

nm. After baking out, the QYs of these individual samples consistently varied only by

factors of 2 or less.

QY results at 0˚ incidence angles were higher than those at 45˚ by about a factor

of 1.2. This could be because the reflectivity of Au at a 0˚ incidence angle is ~1% less

than the reflectivity at 45˚ meaning that a little more light is absorbed at 0˚ that

contributes to the QY.

Commercially polished samples were generally cleaner with a more uniform

surface and did not result in initial increases in QY at 10−6 Torr when a bake-out is first

started on them as in the case of the hand polished samples (see Figures 3-6, 3-8, and

3-9). The hand polished ones likely experienced a quick evaporation of certain

impurities at 130 °C that probably caused an increase of the work function and led to

initially high quantum yields which settled over time.

70

QY measurements made at 240 nm are consistently higher than those made at

250 nm by an average factor of 2.3 ± 0.3 for the samples that were commercially

prepared as shown in Figures 3-11 to 3-14. The resulting Au work function, calculated

using Equation 3-18 was (4.56 ± 0.07) eV, which agrees with expected range of Au

work functions [8].

The 240 nm QY measurements in Figure 3-9 for the hand polished sample 1AP

were higher than those at 250 nm by a factor of ~ 5. A value of ~4.8 eV was estimated

as the work function when Equation 3-18 was used (this particular sample, initially

measured as shown in Figure 3-4, gave inconsistent values varying by factors of 1.2 to

10 when no bake-out was done beforehand in Figure 3-4).

QY measurements were made while pressures in the vacuum chamber were

purposefully varied between the 1 × 10−6 Torr and 3 × 10−8 Torr in order to investigate

if there was a dependence on pressure. No significant change in QY was observed

between 10−8 and 10−7 Torr for all four samples considered, but at 10−6 Torr, two of the

samples showed a reduction in QY of at least a factor of 3. Some sort of balancing effect

seems to be at play as these surfaces are likely to be contaminated with water and

carbon compounds, no effort was made to get rid of the latter except for the bake-out for

these measurements, but one thing that can be said is that water is present in higher

quantities on the surface at 10−6 Torr leading to increased work functions and a lower

QY than at 10−8 Torr. Hence only two out of four samples tested showed a noticeable

dependence on pressure.

Tested alternative coatings; SiC and TiC seem to have properties that would

make them suitable alternatives to Au. Reflectivity values obtained for these coatings [5]

71

indicate that they would be able to absorb sufficient photons and be adequate

alternatives for charge control but their average QYs are lower than that of the Au

samples prepared in the same way by more than a factor of ten with TiC exhibiting the

best stability. Au is the coating choice for LISA because LISA Pathfinder has

successfully demonstrated UV charge control and caging and release by using Au. Other

missions could consider these alternative coating materials in future.

XPS measurements performed on an Au sample cleaned with isopropanol

revealed the likely composition of the surface contaminants to be oxygen and

hydrocarbons. Hydrocarbons are a challenge to get rid of since they are not removed by

a bake-out and have to be subjected to Argon sputtering if there is an absolute need to

get rid of them [21]. Another Au sample surface was treated with a chemically stable self-

assembled monolayer from Dodecanethiol. The purpose of this monolayer was to create

a uniform surface on Au that could result in more repeatable QY measurements. Further

studies would be needed to determine whether this would be useful for LISA or not. The

introduced monolayer described in this chapter did result in QY values in the 10−4 range

and significantly reduced QY variation of a factor of 1.05 with repeated measurements.

Simple reflectivity analyses described in section 3.2 shows that the QYs of

adjacent surfaces used in charge control should be within a factor of three of each other.

This means, for example, that sample 4AP measured as described in Figures 3-11, 3-16

and 3-17 would not be a suitable adjacent match for 4BP, 4CP or 4DP since the QYs of

these samples exhibits more than a factor of three difference at LISA-like pressures of

10−8 Torr.

72

CHAPTER 4 DEMONSTRATION OF DC AND AC UV LED CHARGE CONTROL ON THE UF

TORSION PENDULUM

4.1 Pendulum Description

Investigating the operational TM charge control modes proposed for LISA

requires ground testing. The UF Torsion Pendulum is a laboratory test bed for testing

the operation and performance of GRS technology on ground. The UF torsion pendulum

design is based on the University of Trento pendulum. Key differences for the UF

torsion pendulum include longer inertial members and an incorporated laser

interferometric position readout in addition to the capacitive readout. The capacitive and

interferometric readouts measure the TM displacement with sensitivities of 30 nm/√Hz

and 0.5 nm/√Hz respectively at 1 Hz [29].

The pendulum consists of an inertial member made up of 4 TMs affixed to the

ends of a cross shaped design and suspended by a 1 m long, 50 μm diameter fiber as

shown in Figure 4-1(c). The distance between the center of each TM and the center of

the crossbar is 22.2 cm. The total mass of the suspension is ~ 477 g. The suspended

test masses are hollow, gold-coated 46 mm aluminum cubes, two of which are isolated

inside separate gold-coated aluminum housings. The use of hollow TMs ensures a

reduction in the mass of the pendulum and the required thickness of the suspension

fiber which in turn leads to reduced thermal noise. Accelerations and displacements due

to all the surface forces acting on the pendulum are increased because of the reduced

total mass of the structure which enables them to be better studied and understood [11].

73

Figure 4-1. (a) Pendulum inertial member surrounded by electrostatic shields, (b) Simplified electrode Housing, (c) CAD model of the torsion pendulum, (d) Torsion pendulum assembly enclosed inside the vacuum chamber

The pendulum electrode housing shown in 4-1(b) is a simplified version of the

LISA pathfinder GRS. There are 6 total electrodes with each one centered on the

interior faces of the housing. Ceramic bushings are used to electrically isolate the

electrodes from the structure of the housing. The electrodes are for sensing and

actuating the TMs in three translational degrees of freedom. In the sensitive direction in

which the pendulum rotates about its axis as shown in Figure 4-1(a), the gaps between

the electrodes and the test mass surface are 8 mm. This gap size was chosen in

contrast to the 4 mm gap size in the LPF GRS to minimize interactions between the

GRS and the TM. The 4 mm gap in LPF offers a balance between minimizing the

effects of possible noise due to potentials on the TM surface and the capacitive sensing

74

requirements of 2 nm/√Hz [30]. The 8 mm gap utilized in the torsion pendulum is

designed to minimize these effects even further.

The whole pendulum structure is housed within a 60 cm diameter vacuum

chamber that includes a hollow tube for suspending the TM assembly from the fiber.

The fiber is attached at the top of the tube to both a rotational manipulator to allow for

adjusting the orientation of the pendulum, and a translational XYZ manipulator, to allow

for calibration and centering.

Figure 4-2 shows three UV optical fiber ports incorporated on each electrode

housing to allow for AC and DC charge control on the TMs via UV-light. One port

illuminates the test mass, one illuminates the electrodes, and one illuminates both the

test mass and the electrodes simultaneously.

Figure 4-2. UV light injection geometry for the simplified GRS, Left: UV light illuminates either the TM or the electrodes, Right: UV light simultaneously illuminates both the TM and injection electrodes

The set of electrodes installed on the electrode housing (EH) together with the

TM make up the simplified pendulum GRS. The electrode housing completely

surrounds the TMs. An AC signal can be injected into two of the electrodes to polarize

75

the TM and the polarization is measured by another set of electrodes used for sensing.

The GRS also allows systematic actuation to be carried out on the TMs. If the system of

TMs is decoupled from the gravity of the Earth, it is possible to identify and quantify

many sources of noise in the sensor.

As shown in figure 4-3 (a), for small rotations, the differential displacements of

the two enclosed test masses, x1 and x2 with respect to their individual housings is

defined as 𝜑 through the following equation,

Figure 4-3. (a) Test mass rotation, (b) Test mass swing

(𝑥1− 𝑥2)

2 𝐿=

𝜑 𝐿−(−𝜑 𝐿)

2 𝐿=

2 𝜑 𝐿

2 𝐿= 𝜑 (4-1)

Where 2 L is the total length of the pendulum arm and the z coordinate is defined out of

the page.

The translation of the inertial member in the x direction as shown in Figure 4-3

(b) is defined as the “swing” motion of the pendulum which is calculated as the average

of the corresponding displacements, x1 and x2,

76

x1+ x2

2 (4-2)

4.1.1 Capacitive and Interferometric Readout

The simplified GRS measures the position of the TM by measuring the

capacitance of a set of surrounding electrodes towards the TM. The TMs are polarized

by a 100 kHz sine wave generated by a data acquisition board applied to injection

electrodes on opposite sides of the housing as shown in Figure 4-4. The differential

current measured through the two sensing electrodes is proportional to the

displacement of the TM from the center. The measured current is converted into a

voltage with a transimpedance amplifier which grounds the sensing electrodes with

respect to the TM to ensure that the voltage drop between the TM and electrodes is

only due to the injection voltage. The capacitive sensing and actuation scheme includes

digital to analog electronics (DAC) for generating injection and actuation signals and

analog to digital electronics (ADC) for acquiring readout signals. The digitized signal

from the readout is used to multiply the 100 KHz injection used to polarize the TM. This

digitized signal is also used to multiply the same 100 kHz signal shifted in phase by 90˚.

Cascaded Integrator Comb (CIC) filters are subsequently used to downsample and

integrate the multiplied signals. The In-phase (I) and Quadrature (Q) components of the

resulting vector R (θ), defined by the pendulum’s motion can be modified in such a way

that all the required information is contained in only one of the components of the vector

[12]. Another method of reading out the pendulum’s position is by the use of the

interferometer which measures the angular displacement of the two opposite

unenclosed TMs. The interferometer passes 45° polarized light through a beam splitter

77

(BS) and reflects the beams off them before recombining at a power beam splitter

(PBS) outside the chamber that sends the beam into a polarizing beam splitter and

separates them on two different photodiodes [14].

Figure 4-4. Capacitive and Interferometric read-out scheme, (a) Actuation and capacitive sensing scheme for a pair of electrodes enclosing a single TM, (b) Electrostatic actuation electronics, (c) Interferometric readout scheme for TM position, (d) Layout of interferometer components in the torsion pendulum

4.1.2 Measured Time Series of the Pendulum Rotation Angle

The pendulum angle obtained from the natural free oscillations of the pendulum

as a function of time is shown in Figure 4-5. Sensors record the displacements of the

78

test masses with respect to the equilibrium point of the pendulum and the differential

motion associated with the torsional rotation of the fiber is scaled by the arm length and

expressed as an angle as in Equation 4-1. The natural rotational period of the pendulum

is about 48 minutes.

Figure 4-5. Pendulum angle as a function of time as measured both capacitively and interferometrically

A typical noise run set up overnight yields more than 50000 seconds of data.

Longer stretches are reserved for the weekends and typically yield up to 200000

seconds. The time series from both the capacitive and interferometric readout are

represented in Figure 4-5. A close up view of a section of the time series shows a

sudden change in the pendulum motion due to some fairly regular disturbance torques.

Investigating this disturbance did not yield any interdependence with changes in

temperature, magnetic fields or charge build up on the pendulum test masses but a

correlation was found with sudden increases in pressure as indicated on the pressure

79

gauge. As a result of the sudden change in pendulum motion showing up in the time

series, data analyzed was limited to the segments in between the disturbances.

4.1.3 Pendulum Acceleration Noise Performance

A PID routine first damps the natural oscillation of the pendulum to within tens of

microrads before it is left to oscillate freely without applying any actuation. An LTPDA

algorithm is used to solve the equation of motion of the pendulum and calculate the

corresponding external torque. The torque is divided by the length of the pendulum arm

and the mass of the LISA TMs. The spectrum is then taken to get the equivalent LISA

TM acceleration noise. Another method of finding the acceleration noise would be to

divide the spectrum of phi by the pendulum transfer function to get the torque and then

divide this by the length of the pendulum arm and the arm of the LISA TMs.

Figure 4-6. UF torsion pendulum acceleration noise spectrum

80

The acceleration noise performance for both the interferometric and capacitive

readout with and without the regular disturbances in Figure 4-5 are shown in Figure 4-6,

as well as the fiber thermal noise. Segments between the disturbances provide a

shorter stretch of data than that from a complete weekend run hence the average is

limited to a minimum frequency value of 0.3 mHz.

An acceleration noise plot with lower frequency data obtained from an entire

stretch of weekend data with disturbances included and higher frequency data obtained

from the data in between the disturbances is shown Figure 4-7.

Figure 4-7. LISA requirements compared with the acceleration noise performance of the torsion pendulum facility

The disturbances occur between 1 × 10−4 Hz and 3.5 × 10−4 Hz as indicated by

the gap between the red curve and the blue curve in Figure 4-7. The acceleration noise

estimated for the capacitive readout is about 2 × 10−12 ms−2/√Hz at 0.5 mHz while that

for the interferometric readout is around 4 × 10−13 ms−2/√Hz at 2 mHz. The

81

interferometric result is still a factor of 100 above what is required for LISA and a factor

of 20 above the fiber thermal noise, but similar to other similar facilities, including the

one at the University of Trento.

4.2 Electrostatic Force acting on the Pendulum’s Test Masses and Charge

Measurement

Apart from deliberately polarizing the TMs with bias voltages on the housing

electrodes to induce a charge on them, TM contact with adjacent internal electrode

housing surfaces can impart a potential to the TMs and the ion gauge used to determine

the pressure of the system intermittently can leave the TMs charged as well.

The electrostatic force Fx acting on the TM along the x axis as defined in Figure

4-8, is represented by the formula for the force of attraction between the parallel plates

of a capacitor.

Figure 4-8. Left: TM position with respect to the electrodes, Right: Suspended pendulum

showing the force Fx in the direction of the sensitive axis

𝐹𝑥 = 1

2∑

∂C𝑒

∂𝑥𝑒 (𝑉𝑇𝑀 − 𝑉𝑒)2

(4-3)

Here, 𝐶𝑒 is the capacitance between the TM and the e-th housing electrode (e = 1, 2, 3

…), 𝑉𝑒 is e-th electrode voltage, and 𝑉𝑇𝑀 is the TM potential defined by the combination

82

of the TM voltage due to charge given by 𝑞

𝐶𝑇 and the polarization induced on it due to the

surrounding voltages, ∑𝐶𝑒𝑉𝑒

𝐶𝑇 [11] ;

𝑉𝑇𝑀 = 𝑞

𝐶𝑇 +

1

𝐶𝑇∑ 𝐶𝑒𝑉𝑒𝑒 (4-4)

In Equation 4-4, q is the net charge on the TM and CT is the total capacitance of the TM

towards surrounding surfaces. Considering equal and opposite electrode voltages as

shown in Figure 4-8, 𝑉1 = 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡) and 𝑉2 = − 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡). Equation 4-4 becomes,

𝑉𝑇𝑀 = 𝑞

𝐶𝑇+

1

𝐶𝑇 (𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)(𝐶1 − 𝐶2)) (4-5)

If 𝑋+ and 𝑋− indicate the movement of the TM in the positive and negative X direction

respectively with corresponding capacitances of 𝐶𝑋+ and 𝐶𝑋−

towards an opposite

surface with area A, then for a TM displaced from the center position by 𝑥 as described

by Giacomo Ciani (Diss. Univ. of Trento, 2008)

𝐶𝑋±=

𝜖0𝐴

𝑑∓𝑥 (4-6)

Then,

𝜕𝐶𝑋+

𝜕𝑥|

𝑥=0=

𝐶𝑋+

𝑑 ,

𝜕𝐶𝑋−

𝜕𝑥|

𝑥=0=

−𝐶𝑋−

𝑑 (4-7)

If 𝐶1 = 𝐶𝑋− and 𝐶2 = 𝐶𝑋+

and 𝐶1 = 𝐶2, then ∂C2

∂x=

C

d and

∂C1

∂x=

−C

d .

After substituting for VTM and 𝐶1 and 𝐶2 in Equation 4-3, the force on the pendulum in

the direction of the sensitive axis as derived in appendix C is given by;

𝐹𝑥 = 2𝐶𝑞𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)

𝑑𝐶𝑇 (4-8)

83

Here, A is the amplitude of sinusoidal voltages applied to the electrodes and f is the

frequency of the applied signal. The electrostatic force and the TM motion are related to

the equation of motion of the pendulum for small rotations as given by the second order

ODE,

�� = −𝜔02𝜑 +

𝐿

𝐼𝐹𝑥 (4-9)

Where, ω0 is the natural frequency of the pendulum at (1

48 min), L is the distance

between the point of suspension and the test mass (~0.22 mm), and I is the moment of

inertia(1.63 × 10−2kgm2). Since the pendulum is subjected to an external periodic force,

the particular solution to Equation 4-9 in Appendix C accounts for the forced motion of

the pendulum. It can be represented as,

𝜑𝑝(𝑡) =

2𝐶𝑞𝐴 𝐿

𝑑𝐶𝑇𝐼

𝜔02− (2𝜋𝑓)2 𝑐𝑜𝑠 (2𝜋𝑓𝑡) (4-10)

Where d is the distance between the TM and EH surfaces.

If the measured amplitude of the oscillations in Equation 4-10 is defined as B,

then the resulting net charge q, on the TM can be found as,

𝑞 = 𝐵 𝐶𝑇𝐼 (𝜔0

2− (2𝜋𝑓)2)

2𝐶𝑑𝐴𝐿 (4-11)

In the pendulum, the GRS measures the position of the TM by measuring the

capacitance of the set of electrodes towards the TM which depends on the spacing

between them. Applying a sinusoidal signal directly to the pair of electrodes in the GRS

as shown in Figure 4-8 makes the TM potential oscillate at the same frequency as that

of the driving signal with an amplitude proportional to the amount of charge on the

84

pendulum. For a perfectly centered TM, the capacitances and the currents flowing in

both branches would be equal so that the TM is not attracted towards either of the two

opposing electrodes. A charged TM develops a net force proportional to the TM charge

q, towards the electrodes. A plot of pendulum angle as a function of time is provided in

Figure 4-9.

Figure 4-9. Pendulum angle as a function of time during charge measurement on the pendulum

4.3 Analytical Charge Control Model for the LISA GRS

A variation in the amount of charge on the TM corresponds to a change in its

potential (𝑉𝑇𝑀). As VTM changes, the electron flow rate also changes. It is desirable to

have 𝑉𝑇𝑀 ≈ 0 V to minimize the force noise on the TM, so there is a need to find the

electron flow rate at this value. After considering the surfaces involved in electron

exchange and specifying parameters related to the TM-GRS area illuminated by the UV

85

LED, the analytical model presented here explains the behavior of the TM voltage due

to charge for three cases,

1. It calculates the total electron flow rate ��𝑡𝑜𝑡 when the TM voltage VTM is close to

zero while varying the injection voltage 𝑉𝑖𝑛𝑗 on the electrodes; ��𝑡𝑜𝑡(𝑉𝑖𝑛𝑗 , 𝑉𝑇𝑀 = 0).

2. It determines the electron flow rate at saturation. Here, the voltage on the test

mass is allowed to go to equilibrium while the injection voltage is changing;

𝑉𝑇𝑀(𝑉𝑖𝑛𝑗 , 𝑡 = ∞)

3. It calculates the total electron flow rate when the injection voltage is at a constant

value and the voltage on the TM is changing; ��𝑡𝑜𝑡 (𝑉𝑖𝑛𝑗 = Constant, 𝑉𝑇𝑀).

Sections 4.3.1 and 4.3.2 describe how the model was developed

4.3.1 The Pendulum GRS as a Simplified Parallel Plate Circuit

The electrode housing, the electrodes and the test mass configuration in the

torsion pendulum’s simplified GRS system can be modelled as a simple circuit made up

of parallel plate capacitors. The capacitor plates represent the different surfaces where

the UV light used in charge control is incident. The TM interfaces with both the EH and

injection electrodes surfaces as shown in Figure 4-10. The different surfaces are

labelled i to l:

i. Active injection electrodes surface that faces the TM

j. TM surface that faces the active injection electrodes

k. EH surface that faces the TM

l. TM surface that faces the EH

86

Figure 4-10. Simplified circuit model for charge control

The EH surface which is chosen as the zero reference voltage includes the

grounded non-electrode surfaces. The orientation of the UV light injection ports is

designed to reduce light leakages towards non-zero voltage surfaces that could add

undesirable electron flows. This means that most of the radiation is absorbed after a

certain number of reflections and that transmission effects and light leakages through

non-gold surfaces are neglected. The relatively small gaps between the TM and the EH

of around 8 mm prevent electron absorption by gas ionization in the high vacuum

environment and border effects are minimized because of the design of the electrodes.

Other assumptions are that no electron flow is lost, no border effects at the TM

edges exist and there is no electron cross talk between EH and injection electrodes

since the electrode layout and sizing are optimized to maintain the overall extension

inside a safe-frame smaller than the TM face. In this way, each electrode capacitance

toward the TM does not change appreciably when the TM moves parallel to the

electrode itself. The electrodes are separated from the structure of the housing by a 1

mm groove around each electrode and isolated by ceramic spacers.

87

Surfaces i and j have a controlled electric field from the injection bias on i so that

in addition to the voltage due to charge 𝑞

𝐶𝑇 induced on the TM, an additional offset of

1

𝐶𝑇∑ 𝐶𝑖𝑉𝑖𝑖 due to polarization from the injection surface is included. No polarization

component from the k surface is added since it is grounded and voltages there are zero.

The capacitance of the injection electrodes towards the TM is 𝐶𝑖, 𝐶𝑇 is the total

capacitance and 𝑉𝑖 ≡ 𝑉𝑖𝑛𝑗. This is depicted in Figure 4-11.

Figure 4-11. Electron exchange in a parallel plate configuration

Depending on the value of the injection voltage, the electrons from a surface may

or may not have enough energy to overcome the potential barrier and be successfully

transferred to the other side. If they do have sufficient energy, then the electron flow in

that direction becomes dominant while the other direction is completely suppressed.

The resulting total charge rate on each of the different surfaces therefore includes two

extremes with a transition point in the region where the applied potential barrier is close

to zero.

88

4.3.2 Photoelectron Energy Distribution

The successful extraction and transfer of an electron from one surface to another

depends on the kinetic energy perpendicular to the plates overcoming the potential

barrier ∆V as shown in Figure 4-12.

Figure 4-12. Distribution of energies of emitted electrons in a parallel plate configuration

The energy distributions for electrons emanating from different experimental

geometries have been investigated by Hechenblaikner et al [17] and the distribution of

the normal energies as a function of the applied bias voltage for a parallel plate

configuration was found to be of the form,

𝑓 (∆𝑉) 𝑑𝛥𝑉 = [𝐴𝑛 𝑙𝑜𝑔 (𝑒𝑥𝑝(−∆𝑉+ 𝑉𝑚 )𝑒

𝐾𝑏𝑇 + 1) ] 𝑑𝛥𝑉 (4-12)

Here, An is a constant, e is the charge of the electron, 𝐾𝑏 is Boltzmann’s

constant, ∆𝑉 is the potential difference of the two adjacent surfaces and 𝑉𝑚 = ℎ𝜈−𝜙

𝑒 is

the maximum energy an electron can have after being extracted by a photon of energy

hν from a surface that has a work function of ϕ. Equation 4-12 can be rewritten as,

𝑓 (∆𝑉) ∝ 𝑙𝑜𝑔 (𝑒𝑥𝑝(−∆𝑉+ 𝑉𝑚 )𝑒

𝐾𝑏𝑇 + 1). (4-13)

89

As shown in Figure 4-13, the sign of the potential barrier before V = 0 favors the

movement of electrons in one direction because the electric field is directed in the sense

of that flow, the change in the sign of the potential causes the field to work against the

direction of travel of the electrons and they begin to lose energy until most of them are

unable to overcome the potential barrier. This is referred to as the stopping voltage Vm.

With the exception of the region around the stopping voltage, the function in Equation 4-

13, shown in blue, is well approximated by two straight lines defined in ∆𝑉 ≪ 𝑉𝑚 with a

negative slope and ∆𝑉 ≫ 𝑉𝑚 which is a constant.

The approximation for electrons moving in direction i to j or k to l becomes,

𝑓 (∆𝑉) ∝ −𝑒

𝐾𝑏𝑇(∆𝑉 − 𝑉𝑚) (4-14)

While those electrons moving in direction j to i or l to k are represented as;

𝑓 (∆𝑉) ∝ −𝑒

𝐾𝑏𝑇(−∆𝑉 − 𝑉𝑚). (4-15)

A full derivation of Equation 4-14 and Equation 4-15 can be found in Appendix A.

Figure 4-13. Straight line approximation of the distribution of energies

90

Not all the light sent through the UV light ports is absorbed by the intended

areas. Multiple reflections distribute the total light intensity among the different surfaces.

The TM surfaces are treated as generic surfaces and for a given set of parameters, it

will be straightforward to adapt photoelectron flow rate equations. If positive

contributions are assigned to electrons moving from i to j and negative contributions are

assigned to electrons moving from j to i, then for all the reference surfaces described in

the circuit model in Figure 4-10, the generic expression for the total electron flow rate is,

��𝑡𝑜𝑡 = ��𝑖𝑗 − ��𝑗𝑖 + ��𝑘𝑙 − ��𝑙𝑘 (4-16)

The term ��𝑡𝑜𝑡 is the sum of electron flow rate contributions extended to all

interfaces. ��𝑖𝑗 is the electron flow rate from the i-th surface to j-th surface expressed

in e−

s and so on. The single electron flow rates must be expressed in terms of accessible

quantities. For instance, the general form of nij is related the electrons extracted from

the i-th surface moving towards the j-th surface and can be written as,

��𝑖𝑗 = 𝛼𝑖 𝑎𝑖 𝑄𝑌𝑖(𝜈) 𝐼𝑖 ∙

∫ 𝑔𝑖(𝜈) 𝑑𝜈+∞

𝑒∆𝑉𝑖𝑗+𝜙𝑖ℎ

∫ 𝑓𝑖(𝜙𝑖,∆𝑉𝑖𝑗,𝜈,𝑇)

ℎ𝜈−𝜙𝑖𝑒

∆𝑉𝑖𝑗𝑑∆𝑉𝑖𝑗

∫ 𝑔𝑖(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

∫ 𝑓𝑖(𝜙𝑖,∆𝑉𝑖𝑗,𝜈,𝑇) 𝑑∆𝑉𝑖𝑗


0

(4-17)

Where αi the fraction of the total light intensity is absorbed by the i-th surface and

𝑎𝑖 is the i-th surface area in m2. 𝑄𝑌𝑖(𝜈) is the quantum yield of the i-th surface in e−

γ. This

quantity is assumed to be independent on the voltage applied to the surface but

depends on the surface composition and optical properties. The quantity, 𝐼𝑖 is the total

number of photons per square meter per second (γ

s∙m2) sent to a specific surface with

energy higher than the work function of that surface. The energy distribution of the

91

photons from the UV LED is given by 𝑔(𝜈), the measurement unit is seconds (s). The

radiation frequency ν is in s−1, h is Plancks constant in J ∙ s. The effective work function

of the i-th surface 𝜙𝑖 is in Joules. The energy distribution of the electrons extracted from

the i-th surface at the ij interface as a function of the voltage difference is represented

as 𝑓𝑖. Finally, e is the charge of an electron in Coulombs.

With respect to Equation 4-17, the potential barrier ∆Vij is a function of the

injection electrodes voltage and the TM voltage which can be represented as;

∆𝑉𝑖𝑗 = 𝑉𝑖 − 𝑉𝑗 (4-18)

Where the voltage difference between the two surfaces that the electrons have to

overcome to be successfully transferred to the other side is ∆V and Vi is the potential of

the i-th surface (in Volts),

The resolution of the integrals in Equation 4-17 gives a time differential equation

in 𝑉𝑖 which makes it possible to solve the equation for the voltage due to charge on that

surface. The denominator in Equation 4-17 can be defined as the integral, 𝐷𝑓,𝑖 which

gives the total number of photoelectrons produced with or without enough energy to

overcome the potential barrier. It can be written as,

𝐷𝑓,𝑖 = ∫ 𝑔𝑖(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

∫ 𝑓𝑖(𝜙𝑖, ∆𝑉𝑖𝑗, 𝜈, 𝑇) 𝑑∆𝑉𝑖𝑗


0 (4-19)

If the function 𝑔(𝜈) is known from the photon source characteristics, then for

surface i, the rate of absorption of photons per unit area is calculated according to the

following,

𝐼𝑖 = 𝐼0,𝑖 ∫ 𝑔𝑖(𝜈)𝑑𝜈∞

𝜙𝑖ℎ

(4-20)

92

Where 𝐼0 (in photons per square meter per second) is the total integral area of the

original spectrum

A photon must be absorbed for an electron to be successfully extracted. The

energy distribution of the photons out of the UV LED, g(ν) represents the UV LED

emission spectrum and is well approximated by the Gaussian fit shown in Figure 2-1.

The minimum normal energy the ejected electrons have to overcome to cross the gap

depends on the potential of the originating surface and its work function given by,

|𝑒∆𝑉+𝜙

ℎ|. The combination of the normal energy distribution of extracted electrons

f(𝜙, 𝛥𝑉, 𝜈, 𝑇) and the energy distribution of the photons 𝑔(𝜈) in the numerator, is the

function that counts the number of UV photons that produce electrons with enough

normal energy to overcome the potential barrier. Each illuminated surface considered

receives a different amount of light α with the same frequency distribution. If the system

is closed and no light is transmitted out of it then the injected UV light is completely

absorbed in different portions by the surfaces after consecutive reflections. The ratio of

the double integrals gives the proportion of electrons out of all the extracted

photoelectrons that obtain enough normal energies to overcome the potential barrier

along their path towards or away from the TM surface. The number of electrons

extracted is proportional to the absorbed fraction of light α, the illuminated surface area

A, the UV light intensity 𝑔(𝜈), and the Quantum Yield QY, which takes all the other

effects into account. The quantum yield is a constant with respect to the photon

frequency but it must be integrated along with the other expressions in the double

integral if an analytical expression is found for it.

93

If Equation 4-14 is substituted into Equation 4-17, the equation for the electron

flow rate nij can be written as;

��𝑖𝑗 = 𝛼𝑖 ∙ 𝑎𝑖 ∙ 𝑄𝑌𝑖(𝜈) ∙ 𝐼𝑖

∫ 𝑔(𝜈) 𝑑𝜈+∞


∫− 𝑒

𝐾𝑏𝑇(∆𝑉𝑖𝑗−𝑉𝑚)𝑑∆𝑉𝑖𝑗


∆𝑉𝑖𝑗

∫ 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

∫− 𝑒



0

(4-21)

The photon distribution g(ν) follows a normal distribution with,

𝑔(𝜈) = 1

𝜎√2𝜋𝑒

− (𝜈− 𝜈)2

2𝜎2 (4-22)

Here, ν and 𝜎 are the mean and standard deviation of the distribution respectively. After

evaluating the double integral in Equation 4-21 as shown in Appendix B, the following

substitutions can be made for the final expression in the numerator (for surface i or j

when defined accordingly),

𝐴𝑖 = ∫ 𝑔(𝜈) +∞

𝑒∆𝑉𝑖𝑗+𝜙𝑖

ℎ

𝑑𝜈 (4-23)

𝐵𝑖 = ∫ 𝜈 𝑔(𝜈)+∞


ℎ

𝑑𝜈 (4-24)

𝐶𝑖 = ∫ 𝜈2𝑔(𝜈)+∞


ℎ

𝑑𝜈 (4-25)

For the denominator:

𝐴𝑖𝑑 = ∫ 𝑔(𝜈) +∞

𝜙𝑖ℎ

𝑑𝜈 (4-26)

𝐵𝑖𝑑 = ∫ 𝜈 𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 (4-27)

𝐶𝑖𝑑 = ∫ 𝜈2𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 (4-28)

The terms, A, B, and C will use −𝑒∆𝑉+𝜙

ℎ in the integral limits for electrons going in the

reverse direction. Equation 4-21 can then be written as:

94

��𝑖𝑗 = 𝛼𝑖 ∙ 𝑎𝑖 ∙ 𝑄𝑌𝑖(𝜈) ∙ 𝐼𝑖.𝑒2∆𝑉𝑖𝑗

2𝐴𝑖+(2𝑒𝜙𝑖𝐴𝑖−2𝑒ℎ𝐵𝑖)∆𝑉𝑖𝑗+ℎ2𝐶𝑖−2ℎ𝜙𝑖𝐵𝑖+𝜙𝑖2𝐴𝑖

ℎ2𝐶𝑖𝑑− 2ℎ𝜙𝑖𝐵𝑖𝑑+ 𝜙𝑖2𝐴𝑖𝑑

(4-29)

If Equation 4-15 is substituted into the expression for ��𝑗𝑖 derived in the appendix, the

expression for ��𝑗𝑖 becomes:

��𝑗𝑖 = 𝛼𝑗 ∙ 𝑎𝑗 ∙ 𝑄𝑌𝑗(𝜈) ∙ 𝐼𝑗 ∙

∫ 𝑔𝑗(𝜈) 𝑑𝜈+∞

−𝑒∆𝑉𝑗𝑖+𝜙𝑗ℎ

∫ − 𝑒

𝐾𝑏𝑇(−∆𝑉𝑗𝑖− 𝑉𝑚)

∆𝑉𝑗𝑖

−(ℎ𝜈−𝜙𝑗)

𝑒

𝑑∆𝑉𝑗𝑖


𝜑𝑗ℎ

∫ − 𝑒

𝐾𝑏𝑇(−∆𝑉𝑗𝑖− 𝑉𝑚)

ℎ𝜈−𝜙𝑗𝑒

0𝑑∆𝑉𝑗𝑖

(4-30)

After substituting the modified versions of Equation 4-23 through Equation 4-26 into

Equation 4-30, nji can finally be written as;

��𝑗𝑖 = 𝛼𝑗 ∙ 𝑎𝑗 ∙ 𝑄𝑌𝑗(𝜈) ∙ 𝐼𝑗 𝑒2∆𝑉𝑗𝑖

2𝐴𝑗 −(2𝑒𝜙𝑗 𝐴𝑗 −2𝑒ℎ𝐵𝑗 )∆𝑉𝑗𝑖+ℎ2𝐶𝑗−2ℎ𝜙𝑗𝐵𝑗+𝜙𝑗2 𝐴𝑗

ℎ2𝐶𝑗𝑑− 2ℎ𝜙𝑗𝐵𝑗𝑑 + 𝜙𝑗2𝐴𝑗𝑑

(4-31)

Similar equations can be developed for nkl and nlk by following the same process.

4.3.3 Implementing The Charge Control Model in MATLAB

Experimental data from charge control measurements on the pendulum was

imported into a MATLAB script for comparing with the calculated total electron flow rate

developed from the model in Equation 4-16. This script calls individual functions that

calculate electron flow rates on the individual surfaces described in section 4.3.1. A

likelihood function for determining if the model could explain the actual data was used to

fit parameters such as the area of the GRS / TM system illuminated by the UV LED and

the work function after providing an initial best guess close to the actual expected value

for the required fitting parameters. The likelihood function is finally maximized to

improve the chances of finding fitting parameters that make the observed experimental

results more probable.

95

4.4 DC Charge Control Demonstration on the UF Torsion Pendulum

For the TM charge measurements and control, a LabVIEW Virtual Instrument

(VI) was created with an interface that allowed an amplitude and frequency to be

specified for the equal and opposite sinusoidal voltages applied to opposing x-injection

electrodes. These voltages polarize the TMs with a force described by Equation 4-8. If

the TM is centered and discharged within the GRS, attractive forces from the TM

towards the two opposite electrodes are equal and they cancel out but if this is not the

case, the result is a force that causes a displacement of the TM. The amplitude of this

displacement is proportional to TM charge. Demodulating the TM displacement allows a

measurement of the TM charge to be obtained. Another VI allows the position of the TM

with respect to the center or equilibrium position to be read out.

In the case of charge control at DC, If UV light is used to illuminate the TM,

electrons are transferred from the TM to the electrode housing and the TM voltage due

to charge becomes more positive. The reverse is the case if the electrode housing is

illuminated. Preliminary DC charge control experiments carried out on the pendulum’s

TM prove that UV LED charge control can be done on a LISA test bed as illustrated by

actual measurements presented in Figure 4-14. The initial voltage due to charge was

0.8 V. The electrodes were then illuminated with the UV LED driven at 0.8 mA

equivalent to less than 1 µW of UV power to enhance the flow of photoelectrons from

electrodes to TM. The voltage on the TM was − 2.4 V over 30 minutes and the process

is reversed by illuminating the test mass with 0.8 mA until equilibrium is reached at 0.8

V. The whole procedure can be repeated until the desired voltage due to charge within

the bounds of saturation is reached. Spikes in the data are usually due to someone

96

physically approaching the pendulum or making adjustments to the current driver while

regulating the intensity of the UV LED.

Figure 4-14. Pendulum charge during DC charge control operations on the UF torsion pendulum

4.5 AC Charge Control With The UF Torsion Pendulum

In the case of AC charge control, only one UV light injector would be needed to

illuminate either the TM, the injection electrode or both. The UV LEDs are switched on

only when the electric field in the illuminated section supports the preferred direction of

discharge and prevents the movement of photoelectrons in the other direction [5].

Figure 4-15. Left: UV LED emission out of phase with respect to the injection signal Right: UV LED emission in phase with respect to the injection signal

97

For negative charge transfer, when the 100 kHz signal on the injection electrodes

is in the negative half of the period as shown on the left in Figure 4-15, the UV light is

switched on (out of phase) and the electrons generated within that interval experience a

negative offset that repel the electrons towards the TM so that it becomes negatively

charged. In the case of positive charge transfer, the output of the UV light is shifted in

phase resulting in the electrons being repelled away from the TM. The duty cycle is

mostly kept at a minimum of 5% so that the voltages at a particular set phase with

respect to the injection cycle can be considered as roughly constant as the phase is

varied from 0˚ to -180˚ (right to left).

In the AC charge control demonstration on the torsion pendulum provided in

Figure 4-16, the amplitude of the UV LED voltage with respect to the injection was set in

phase at 0° while being driven at 10 mA (~180 nW), and a 5% duty cycle at the

beginning of the experiment using the UV port illuminating both the TM and the

electrodes. This caused the charge on the TM to become more positive. Using the

same parameters but out of phase at −180° made the voltage due to charge go in the

opposite direction.

98

Figure 4-16. Test mass potential during AC charge control experiment

There is presently a limit on the ability to push the voltage due to charge both

positive and negative while using the charge control port that illuminates both the TM

and electrodes for the following likely reasons; the injection voltage on the pendulum

which was previously set at an amplitude of ± 10 V is now currently set at an amplitude

of ± 3.5 V. This is because the maximum value of the injection voltage sets the limit on

the voltage due to charge acquired by the test mass. This has resulted in equilibrium

voltages as high as ± 4.5 V that cause the pendulum to go unstable due to positive or

negative charge on the TM relative to the housing. Another probable reason is the area

illuminated by UV light being too shallow such that directed UV photons are not

satisfactorily absorbed by intended surfaces. Variations in quantum yield on the

opposing illuminated surfaces also likely contribute to this effect since the present TM

surfaces and opposing electrodes and housing surfaces were not polished to the same

99

specification and probably have different surface properties. These issues are being

addressed in a new, more flight-like GRS to be installed around one of the TMs. It

includes provision for the UV light to be injected at a steeper angle. The surfaces of

both the TMs and the inside of the new GRS are also polished to the same

specification. One of the two current gravitational reference sensors will be left in place

so that its performance can be compared with the new one.

4.5.1 AC Charge Control Experiments With Varying UV Phase

If the duty cycle of the UV LED output with respect to the injection voltage is small

enough, the injection voltage can be considered as equivalent to the set phase of the

UV LED through the following relationship,

𝑉𝑖𝑛𝑗 = 𝐴 ∗ 𝑐𝑜𝑠(𝑃ℎ𝑎𝑠𝑒) (4-32)

Where A is the amplitude of the injection voltage set to a value of 3.5 V

If the output of the UV LED is varied in phase with respect to the injection voltage

while keeping the duty cycle and amplitude constant, the voltage due to charge on the

TM becomes more positive until it reaches equilibrium. On the other hand, the TM

voltage becomes more negative if the output of the UV LED is out of phase with respect

to the injection. Interestingly, the equilibrium voltage due to charge settles at different

values for each phase adjustment. Figure 4-17 shows that the TM saturation voltages

when the UV LED is driven at 15 mA (~ 300 nW) and a 5% duty cycle, go to different

values for 0° phase (equivalent to an injection voltage of 3.5 V), − 22° phase (equivalent

to an injection voltage of 3.24 V) and − 58° phase (equivalent to an injection voltage of

1.85 V) while using the TM-EH UV port for AC charge control measurements. The final

saturation voltage therefore depends on the initial potential barrier (∆V).

100

Figure 4-17. TM Potential while illuminating the AC port with pulsed UV light while varying the phase with respect to the injection voltage.

4.5.2 Measuring Saturation Voltage as a Function of UV Light Injection

In the effort to continue investigating why the TM-Injection electrodes UV port did

not allow for charge to be moved both positive and negative, AC charge control

experiments were carried out by also using the UV ports meant to shine light individually

at either the electrodes or the TM. For measurements made by using the TM port, TM

potential remained in the positive region but stayed in the negative region when the

injection electrodes port was used. In either case, AC charge control is possible

regardless of which of the surfaces is illuminated. This means that reflections between

opposing surfaces illuminated by the UV LED turn out to be an advantage, because the

intended Au surface reflects a percentage of the incident UV light towards the opposing

surface and depending on the work function of that surface, electrons are emitted. This

works out in the way that the TM–Injection electrodes port was originally intended to

101

work because the whole idea was to take advantage of the available 100 kHz injection

field to move the charge from one surface to the other while two surfaces are

simultaneously illuminated.

Test mass saturation voltages obtained were subsequently plotted as a function

of phase for the three existing UV ports as shown in Figures 4-18, 4-19 and 4-20. These

plots were obtained by doing fits to voltage due to charge time series data such as is

shown in Figure 4-17 to determine their eventual saturation values while the phase was

varied from 0˚ to −180˚ ( + 3.5 V to − 3.5 V injection voltage) in 18˚ adjustments. In

plotting Figures 4-18, 4-19 and 4-20, most of the data with saturation voltages that

converged close to 0 V did not require a fit since the UV light could be used to illuminate

the surface long enough for the saturation voltage to be easily reached.

Figure 4-18. Saturation voltage Vs. UV light phase using the electrodes port

102

Figure 4-19. Saturation voltage Vs. UV light phase using the TM port

Figure 4-20. Saturation voltage Vs. Phase using the TM-Injection electrodes port

103

It is interesting to note that the voltage due to charge on the TM can be kept close

to zero by just setting the phase of the UV light at a certain value depending on which

UV port is being utilized. Setting the phase of the UV light from 0° to −90° (which is

equivalent to a potential barrier of 3.5 V to 0 V through Equation 4-32) for both the TM-

Injection electrodes port and the electrodes port ensured that the TM voltages were

close to zero all the time. Setting the phase from − 90° to −180° (0 V to − 3.5 V

injection voltage) for the TM port gave similar results.

4.5.3 Charge Rate

The charge rate can be calculated from the voltage time series plots obtained

during charge measurements. This is especially important for the region where the

voltage on the TM crosses zero because LISA TMs will be kept close to 0 V all the time.

Since the ability to move the TM potential to both positive and negative values on the

pendulum by using a single UV injection port is currently limited (as discussed in section

4.5) by the possibility of differences in QY between the TM and the electrode housing

surfaces and the inability of the directed UV light to be absorbed by the intended

surfaces, the only way to handle the process was by going through the following steps

as demonstrated in Figure 4-21,

1. Start the measurements when the TM is at a negative voltage and then use the

TM port to illuminate the TM to enable the voltage eventually settle at the

saturation value on the positive side for the set phase. The rate of change of the

TM voltage when the voltage crosses zero is then the charge rate for the TM port

at that phase.

104

2. When using the electrodes port, the measurements were started with the voltage

on the TM positive. The electrodes were then illuminated at a particular phase

and the TM voltage allowed to settle at the saturation voltage on the negative

side. The rate of change of the TM voltage when it crosses zero is the charge

rate for the electrode housing port at that set phase.

Figure 4-21. TM voltage as a function of time when using the TM port and EH port to move the voltage due to charge on the TM positive and negative

A combination of the above methods can be used to get the TM voltage due to

charge to move positive or negative by using the TM and electrodes housing port.

Quadratic and exponential fits were done to each of the resulting curves to determine

the charge rate at VTM = 0. The resulting charge rates for the three UV ports with the

105

injection voltage varying from 0˚ through −180˚ are fitted to the analytical model as

discussed in the following sections.

4.6 Fitting Analytical Charge Control Model to Data

The analytical charge control model described in section 4.3 was fit to charge

measurement data obtained from AC charge control experiments using the pendulum’s

UV injection ports as described in section 4.5. Cases one to three below show the

model compared with measurements of voltage due to charge on the test masses.

Phase values from 0˚ to −180˚ were converted to Vinj through Equation 4-32.

4.6.1 Case 1: ��𝒕𝒐𝒕 (𝑽𝒊𝒏𝒋 , 𝑽𝑻𝑴 = 𝟎)

Figure 4-22. UV light injection geometry and circuit model for calculating ��𝑡𝑜𝑡 with

varying 𝑉𝑖𝑛𝑗 and 𝑉𝑇𝑀 = 0

The charge flow rate (V/s) when the voltage due to charge on the TM is zero is

calculated at different values of Vinj when the UV light is used on the electrodes housing

port as shown Figure 4-22. The term Vinj is equivalent to the potential barrier between

the TM and the injection surface when the voltage on the TM is only due to the induced

106

polarization offset. A plot of the charge rate of the pendulum test mass as a function of

the applied potential barrier is presented in Figure 4-23. This plot also includes the

analytical model fitted to the data. The fit was done as described in section 4.3.3.

Figure 4-23. Measured test mass charge rate versus the potential barrier and the best fit model for the electrodes port

Figure 4-24 shows the electron flow rates on the individual surfaces in the system

as described by the analytical model when fitted to the experimental data from the

pendulum. In the negative half of the cycle where the potential barrier is between

− 3.5 V and 0 V, all the electrons from the electrodes surface (i) make it to the TM (j)

because the electrical field is directed in the sense of the flow and encourages the

movement of the electrons. The change in the sign of the potential begins to work

against the direction of electron motion when ∆𝑉 > 0 V. The electrons begin to have

insufficient energy and slowdown from 0 V until they are completely suppressed and

107

none of them make it to the TM by the time the potential is 2 V. The reverse is the case

for the movement of electrons from the TM (j) to the electrodes (i) in the negative half of

the cycle. The electrons here are mostly suppressed between − 3.5 V and −2 V. Some

of them begin to have enough energy to make it to the electrodes surface after ∆𝑉 =

2 V. As soon as the potential barrier becomes 0 V or greater, the sign of the potential

barrier helps all the photoelectrons make it to the electrodes surface in the positive half

of the cycle between 0 V and 3.5 V.

Figure 4-24. Measured test mass charge flow rate as a function potential barrier for each surface when UV light is directed towards the electrodes

There is no applied electric field in the region between the EH surface (k) and the

adjacent TM surface (l), which represents the small area of the grounded EH that faces

the TM which is illuminated along with the injection electrodes. Hence, in both the

negative and positive half of the potential barrier as shown in Figure 4-24, electrons

emitted from the EH remain mostly suppressed to a negligible value. Those produced

by the TM are successfully transferred in the negative half. The electric field working

-4 -3 -2 -1 0 1 2 3 4-6

-5

-4

-3

-2

-1

0

1

2

3

4x 10

-3

deltaV (V)

dV

/dt

ij, INJ-TM

ji, TM-INJ

kl, EH-TM

lk, TM-EH

Total electron flow rate

108

against the direction of flow in the positive half causes the electrons to gradually have

insufficient energy. The term, 1

𝐶𝑇∑ 𝐶𝑖𝑉𝑖𝑖 dominates in this case and is responsible for

the more gradual slope and offset.

The sum total of the electron flow rate which was compared to experimental data

in Figure 4-23 makes sense from an AC charge control standpoint because as expected

in the negative half of the cycle corresponding to when the UV LED is out of phase with

respect to the injection, the movement of electrons from the injection electrodes surface

to the TM surface is dominant while those moving from the TM to the electrodes are

mostly suppressed. The opposite is the case in the positive half of the cycle.

Figure 4-25 shows the charge rate (V/s) as a function of the applied potential

when the analytical model is fitted to AC charge control data from the TM injection port.

The contributions of the electron flow rates from the individual surfaces in the system as

described by the analytical model is shown in Figure 4-26. In the negative half of the

cycle, the electric field works against the direction of the flow of electrons moving from

TM (j) to electrodes (i) but when the sign of the potential changes, the field favors the

direction of travel of the electrons such that all electrons emitted from the TM (j) make it

to the electrodes (i). The reverse is true for the electrons emitted from the electrodes (i)

which have an advantage due to the electric field in the first half of the cycle when

∆ 𝑉 < 0 but gradually lose energy in the second half after the sign of the potential

changes. Electrons moving from the EH (k) to the TM (l) are suppressed in the negative

half of the cycle but all the electrons from the TM (l) make it to the EH (k). When the

sign of the potential changes, all electrons from k make it to l while those moving from l

to k are gradually suppressed.

109

Figure 4-25. Measured charge rate vs. phase using the TM port and best fit model to the data

Figure 4-26. Measured charge flow rate for each surface from TM port and best fit model

-4 -3 -2 -1 0 1 2 3

0

2

4

6

8

10

12

14

x 10-3

deltaV (V)

dV

/dt

ij, INJ-TM

ji, TM-INJ

kl, EH-TM

lk, TM-EH

Total electron flow rate

110

The total electron flow rate which was compared to experimental data in Figure

4-25 makes sense in this case as well because, as expected, in the negative half of the

cycle corresponding to when the UV LED is out of phase with respect to the injection,

the movement of electrons from the injection to the TM surface is dominant while those

moving from the TM to the injection electrodes are mostly suppressed. The opposite is

the case in the positive half of the cycle.

4.6.2 Case 2: 𝑽𝑻𝑴 (𝑽𝒊𝒏𝒋 , 𝒕 = ∞)

Here, the model is used to describe the case where the voltage on the TM is

allowed to go to saturation for changing values of the potential barrier while the

electrodes housing is illuminated. In the first half of the cycle where the potential barrier

is between −3.5 V and 0 V in Figure 4-27, the electric field favors the movement of

electrons towards the TM until the equilibrium voltage for the corresponding value of Vinj

is reached (or until total charge flow rate equals zero at the set Vinj). The voltage on the

TM is maintained close to 0 V after the sign of the potential barrier changes. Therefore,

the total charge flow rate is close to zero for all Vinj in the positive half of the cycle.

When the TM is illuminated, the voltage due to charge on the TM remains close

to 0 V in the negative half of the cycle because the electric field favors the movement of

electrons away from the TM. Therefore, the charge flow rate at equilibrium is similar for

all values of ∆ V in the negative half of the cycle, as shown in Figure 4-28. When the

sign of the potential changes, the TM begins to accumulate excess electrons and the

charge flow rate at equilibrium is not similar for all values of Vinj in the positive half of the

cycle.

111

Figure 4-27. TM Voltage at equilibrium for different values of the potential barrier on the electrodes port

Figure 4-28. TM Voltage at equilibrium for different values of potential barrier when using the TM port

112

4.6.3 Case 3: ��𝒕𝒐𝒕 (𝑽𝒊𝒏𝒋 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕, 𝑽𝑻𝑴)

This section examines the charge flow rate (V/s) when the voltage due to charge,

𝑞

𝐶𝑇 on the TM is allowed to go to a saturation value determined by a known constant

potential bias as described in section 4.6.2. The total test mass voltage becomes a

contribution of the voltage due to charge 𝑞

𝐶𝑇 and the polarization from the injection,

1

𝐶𝑇∑ 𝐶𝑖𝑉𝑖𝑖 as shown in Figure 4-29.

Figure 4-29.Circuit model showing the TM voltage as a contribution of the voltage due to charge and the TM polarization due to the injection voltage

The measured voltage time series shown in Figures 4-30 and 4-31 respectively,

provide the charge flow rate calculated as the TM voltage approaches saturation from

both the negative and positive regions when the electrodes port is used. In Figure 4-30,

the slope of the curve from −1.6 V all the way to − 0.6 V is calculated. At −0.6 V the TM

has reached its saturation voltage and the charge rate is zero. The charge rates from

+1.8 V to − 0.6 V in Figure 4-31 was also found by calculating the charge rates along

the curve as the voltage moved to its saturation value.

113

Figure 4-30. Voltage time series as TM voltage approaches saturation from below

Figure 4-31. Voltage time series as TM voltage approaches saturation from above

All the slopes derived in this way are plotted with their corresponding TM

voltages shown in Figure 4-32 with the corresponding model fit to the data. The side of

114

the plot to the left of − 0.6 𝑉 has a more gradual slope because the TM approaches

saturation gradually over 25000 seconds as shown in Figure 4-30. Therefore the

change in the charge rate (V/s) converted to apparent yield (electrons per photon) from

the starting TM voltage to saturation at − 0.6 𝑉 is only about a factor of 0.3. The

apparent yields to the right of − 0.6 V were calculated from the data in Figure 4-31. The

charge rates here change more drastically because the TM approaches saturation more

quickly in about 10000 seconds with the change in apparent yield being more than a

factor of 3.

Figure 4-32. Measured charge flow rate and best fit model as test mass voltage changes at a constant potential bias when using the electrodes housing port

A similar behavior is observed when the TM UV port is used. Figure 4-33 shows

the best fit model to the measured data for this case. The saturation voltage on the test

115

mass is around 1.16 V. The apparent yield above this value shows a pronounced

change in apparent yield from the starting point to the equilibrium value of about a factor

of 1.5. This is similar to the change in apparent yield obtained below the saturation

value.

Figure 4-33. Charge flow rate as the test mass voltage changes at a constant potential bias when using the TM port

4.7 Conclusions

Charge build-up on the TMs in the Torsion pendulum was successfully controlled

in two ways: by illuminating either the electrodes housing or the TM with constant (DC)

UV light, and by synchronizing the output of the UV LED with the 100 KHz injection

signal (AC charge control).

An analytical model was developed for calculating the total electron flow rate

within the GRS as a function of the applied potential on the injection electrodes. This

116

model can be modified for the case when the voltage on the TM is zero while

accounting only for the polarization induced on the TMs from the electrodes. It can also

be modified for the case when the voltage on the TM is allowed to evolve until it reaches

equilibrium. The model adequately explained the AC charge control data obtained from

the pendulum within a reasonable margin of error. Further developments to this model

will include ray tracing to determine the area illuminated by the UV light inside the

sensor and track the number of photoelectrons. The results of the ray tracing will then

be incorporated into a numerical charge control model

The results obtained indicated that the UV port illuminating both the TM and the

electrodes housing were likely so shallow that the photoelectrons seemed to pass

though the region without hitting the intended surfaces. A new flight-like GRS will be

installed to compare with one of the simplified ones to help with obtaining results more

compatible with LISA expectations.

117

CHAPTER 5 SUMMARY OF CONCLUSIONS INCLUDING RECOMMENDATIONS FOR FUTURE

WORK

The proposed charge control scheme for LISA will use the principle of

photoelectric effect to remove excess test mass charge by illuminating the relevant

surfaces with UV light in order to generate a flow of electrons in the desired direction.

The effectiveness of this process depends on the quantum yield (QY) of the surfaces.

The QY depends on the energy of the illuminating photons, the work function of the

illuminated surface, the reflectivity of the surfaces and the number of electrons that

successfully cross the gap between the illuminated surface and the opposite surface.

One of the arguments for using UV LEDs in charge control is their availability at lower

wavelengths of 240 nm and 250 nm compared with Hg lamps which have a wavelength

of 254 nm. A part of this work focuses on quantifying the QYs of several Au samples at

240 nm and 250 nm as a function of time, temperature, and vacuum pressure. The LISA

test plan can then account for possible QY changes related to these parameters.

After several Au samples were repeatedly baked-out at 130 °C, their QYs went

from varying by a factor of ten before baking out to varying by less than a factor of two

afterwards. This is useful, because after the LISA GRS is baked out in vacuum before

integration, surface contamination will be reduced and the quantum yield will be

stabilized.

The simplified GRSs in the torsion pendulum assembly have been operating at

the base pressure of around 10−6 Torr. This is a factor of one hundred above what LISA

requires. The new flight like GRS to be installed will also likely be operated at the same

pressure. It is therefore important to investigate if the QYs of tested Au samples have a

significant dependence on pressure. Four Au samples which were prepared in the same

118

way were each measured at three different vacuum pressures. Results showed that a

pressure increase from 10−8 Torr to 10−6 Torr resulted in a decrease in QY of at least a

factor of three for two out of the four samples. After concluding measurements at 10−6

Torr on one of the Au samples tested, additional long term measurements of more than

1000 hours were conducted on the same sample at 10−8 Torr without breaking vacuum.

Results show that the QYs for long term measurements at 10−8 Torr dropped by a

factor of two below what the average was at 10−6 Torr. While this measurement is only

for one sample, this is important because LISA pressures could rise to values as high

as 10−5 Torr before launch due to vacuum leaks. The pressure is expected to drop back

to 10−8 Torr after it is vented to the space environment. It is important to take changes

as a result of expected pressure variations into account.

Adjacent surfaces participating in electron exchange in LISA may differ too much

in QY if care is not taken. If this is the case, electrons may move in the unintended

direction and complicate the charge control process. The results of simple reflectivity

analysis on adjacent Au surfaces described in this work show that the QY of the

illuminated surface should be greater than that of the adjacent surface by a factor

determined by the common reflectivity of both surfaces if their reflectivities are equal. If

the reflectivities are different, then the factor is determined by the reflectivity of the

adjacent surface.

It is reasonable for the GRS system in LISA to be represented as a circuit

composed of parallel plate capacitors for describing individual surfaces that undergo

illumination during charge control. The GRS system in the torsion pendulum test bed

119

was modelled as such to provide a means of describing the photon energy distribution

and electron exchange process during charge control.

DC charge control experiments were carried out by using 240 nm UV LEDs to

either illuminate the TM or the electrodes in the pendulum’s simplified GRS system. The

direction of illumination would be determined by the initial voltage on the TM. The

results discussed in section 4.4 prove that bipolar discharge is possible for LISA, using

UV LEDs.

For AC charge control, the power output of the UV LED was synchronized with

the 100 kHz injection voltage already present in the GRS for capacitively reading out the

positions of the TMs with respect to the housing. AC charge control experiments carried

out by using all available UV ports demonstrate that the voltage due to charge on the

TM can be controlled depending on the phase, amplitude and duty cycle of the UV

power output with respect to the injection signal.

An analytical charge model was developed for calculating the total charge flow

rate as a function of applied potential. The model could be modified for three different

cases. One of which is the calculation of the charge flow rate when the voltage on the

TM is close to zero. This is important because the aim is to keep LISA test masses

close to zero volts at all times. Despite the GRS being a simplified version of what is

required for LISA, the model adequately explained data obtained from the different UV

injection ports with the margin of error increasing for situations where the voltage on the

TM is far from zero.

A new flight-like GRS system has been designed and developed at the University

of Florida. This will be installed in the pendulum to compare with one of the existing

120

simplified ones. Further developments to the analytical model will include multi physics

finite element analysis and ray tracing to more accurately determine the area illuminated

by the UV light inside the GRS and track the number of photoelectrons. The results of

this analysis will then be incorporated into a numerical model to obtain results that are

more representative for LISA.

121

APPENDIX A DISTRIBUTION OF ELECTRON ENERGIES AS A FUNCTION OF APPLIED

BIAS VOLTAGE

The distribution of the normal energies as a function of the applied bias

voltage for a parallel plate configuration is of the form,

𝑓 (∆𝑉) 𝑑𝛥𝑉 = [𝐴𝑛 𝑙𝑜𝑔 (𝑒𝑥𝑝(−∆𝑉+ 𝑉𝑚 )𝑒

𝐾𝑏𝑇 + 1) ] 𝑑𝛥𝑉 (A-1)

Here, 𝐴𝑛 is a constant, e is the charge of the electron, 𝐾𝑏 is Boltzmann’s

constant, ∆𝑉 is the potential difference of the two adjacent surfaces

𝑉𝑚 = ℎ𝜈−𝜙

𝑒 (A-2)

The expression for 𝑉𝑚 represents the maximum energy an electron can have

after being extracted by a photon of energy ℎ𝜈 from a surface that has a work

function of 𝜙. Equation A-1 can be rewritten as,

𝑓 (∆𝑉) ∝ 𝑙𝑜𝑔 (𝑒𝑥𝑝(−∆𝑉+ 𝑉𝑚 )𝑒

𝐾𝑏𝑇 + 1) (A-3)

𝑑𝑓(∆𝑉)

𝑑∆𝑉 = −

𝑒

𝐾𝑏𝑇 (

𝑒𝑥𝑝

−(∆𝑉−𝑉𝑚)𝑒𝐾𝑏𝑇

𝑒𝑥𝑝

−(∆𝑉−𝑉𝑚)𝑒𝐾𝑏𝑇 +1

) (A-4)

If ∆V>>𝑉𝑚 or ∆V+∞

𝑑𝑓(∆𝑉)

𝑑∆𝑉= 0 (A-5)

If ∆V<<𝑉𝑚 or ∆V-∞

𝑑𝑓(∆𝑉)

𝑑∆𝑉= −

𝑒

𝐾𝑏𝑇∗ 1 (A-6)

The function in Equation A-1, shown in blue, is well approximated by two

straight lines defined as ∆𝑉 ≪ 𝑉𝑚 with a negative slope and ∆𝑉 ≫ 𝑉𝑚 which is a

constant.

122

Figure A-1. Illustration of straight line approximation of Equation A-1

If the equation of the given straight line with intercept β is written as,

𝑓 (∆𝑉) = −𝑒

𝐾𝑏𝑇∆𝑉 + 𝛽 (A-7)

And

𝑓 (𝑉𝑚) = −𝑒

𝐾𝑏𝑇𝑉𝑚 + 𝛽 = 0 (A-8)

Find intercept β = 𝑒

𝐾𝑏𝑇𝑉𝑚

For electrons moving from i to j;

𝑓 (∆𝑉) = −𝑒

𝐾𝑏𝑇(∆𝑉 − 𝑉𝑚) (A-9)

And for electrons moving from j to i;

𝑓 (∆𝑉) = −𝑒

𝐾𝑏𝑇(−∆𝑉 − 𝑉𝑚) (A-10)

123

APPENDIX B SOLUTIONS TO PHOTOELECTRON FLUX EQUATIONS

The general form of ��𝑖𝑗, which is related the electrons extracted from the i-

th surface towards the j-th surface can be written as,

��𝑖𝑗 = 𝛼𝑖 ∙ 𝑎𝑖 ∙ 𝑄𝑌𝑖(𝜈) ∙ 𝐼𝑖

∫ 𝑔(𝜈) 𝑑𝜈+∞


∫− 𝑒



∆𝑉𝑖𝑗

∫ 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

∫− 𝑒



0

(B-1)

Numerator of the integral ratio in Equation B-1;

1

2𝐾𝑏𝑇𝑒 (ℎ2 ∫ 𝜈2𝑔(𝜈) 𝑑𝜈

+∞


ℎ

− 2ℎ𝜙𝑖 ∫ 𝜈 𝑔(𝜈) 𝑑𝜈+∞


ℎ

+ 𝜙𝑖2 ∫ 𝑔(𝜈) 𝑑𝜈

+∞


ℎ

+

𝑒2∆𝑉𝑖𝑗2 ∫ 𝑔(𝜈) 𝑑𝜈

+∞


ℎ

− 2𝑒∆𝑉𝑖𝑗ℎ ∫ 𝜈 𝑔(𝜈) 𝑑𝜈 + 2𝑒∆𝑉𝑖𝑗𝜙𝑖

+∞


ℎ

∫ 𝑔(𝜈) 𝑑𝜈+∞


ℎ

)

(B-2)

Denominator of the integral ratio in Equation B-1;

1


+∞𝜙𝑖ℎ

− 2ℎ𝜙𝑖 ∫ 𝜈 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

+ 𝜙𝑖2

∫ 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑖ℎ

(B-3)

Define Ai, Bi and Ci for Equation B-2 and Aid, Bid and Cid for Equation B-3 as,

𝐴𝑖 = ∫ 𝑔(𝜈) +∞


ℎ

𝑑𝜈 (B-4)

𝐵𝑖 = ∫ 𝜈 𝑔(𝜈)+∞


ℎ

𝑑𝜈 (B-5)

𝐶𝑖 = ∫ 𝜈2𝑔(𝜈)+∞


ℎ

𝑑𝜈 (B-6)

𝐴𝑖𝑑 = ∫ 𝑔(𝜈) +∞

𝜙𝑖ℎ

𝑑𝜈 (B-7)

𝐵𝑖𝑑 = ∫ 𝜈 𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 (B-8)

124

𝐶𝑖𝑑 = ∫ 𝜈2𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 (B-9)

Equation B-1 becomes;

��𝑖𝑗 = 𝛼𝑖 ∙ 𝑎𝑖 ∙ 𝑄𝑌𝑖(𝜈) ∙ 𝐼𝑖.𝑒2∆𝑉𝑖𝑗

2𝐴𝑖 + (2𝑒𝜙𝑖𝐴𝑖 − 2𝑒ℎ𝐵𝑖)∆𝑉𝑖𝑗 + ℎ2𝐶𝑖 − 2ℎ𝜙𝑖𝐵𝑖 + 𝜙𝑖2𝐴𝑖

ℎ2𝐶𝑖𝑑 − 2ℎ𝜙𝑖𝐵𝑖𝑑 + 𝜙𝑖2𝐴𝑖𝑑

(B-10)

For electrons extracted from the j-th surface;

��𝑗𝑖 = 𝛼𝑗 ∙ 𝑎𝑗 ∙ 𝑄𝑌𝑗(𝜈) ∙ 𝐼𝑗 ∙


−𝑒∆𝑉𝑖𝑗+𝜙𝑗

ℎ

∫ − 𝑒

𝐾𝑏𝑇 (−∆𝑉𝑖𝑗 − 𝑉𝑚)∆𝑉𝑖𝑗

−(ℎ𝜈−𝜙𝑗)

𝑒

𝑑∆𝑉𝑖𝑗


𝜑𝑗

ℎ∫ −

𝑒𝐾𝑏𝑇 (−∆𝑉𝑖𝑗 − 𝑉𝑚)

ℎ𝜈−𝜙𝑗

𝑒0

𝑑∆𝑉𝑖𝑗

(B-11)

Numerator of the integral ratio in Equation B-11;

1


+∞𝑒∆𝑉𝑖𝑗+𝜙𝑗

ℎ

− 2ℎ𝜙𝑗 ∫ 𝜈 𝑔(𝜈) 𝑑𝜈+∞

𝑒∆𝑉𝑖𝑗+𝜙𝑗

ℎ

+ 𝜙𝑗2

∫ 𝑔(𝜈) 𝑑𝜈+∞


ℎ

+

𝑒2∆𝑉𝑖𝑗2

∫ 𝑔(𝜈) 𝑑𝜈+∞


ℎ

+

2𝑒∆𝑉𝑖𝑗ℎ ∫ 𝜈 𝑔(𝜈) 𝑑𝜈 − 2𝑒∆𝑉𝑖𝑗𝜙𝑗+∞


ℎ

∫ 𝑔(𝜈) 𝑑𝜈) +∞


ℎ

(B-12)

Denominator of Equation the integral ratio in B-11;

1


+∞𝜙𝑗

ℎ

− 2ℎ𝜙𝑗 ∫ 𝜈 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑗

ℎ

+ 𝜙𝑗2

∫ 𝑔(𝜈) 𝑑𝜈+∞

𝜙𝑗

ℎ

(B-13)

Define Aj, Bj and Cj and Ajd, Bjd and Cjd for Equation B-12 and Equation B-13 by

replacing the indexes accordingly to get;

125

��𝑗𝑖 = 𝛼𝑗 ∙ 𝑎𝑗 ∙ 𝑄𝑌𝑗(𝜈)

∙ 𝐼𝑗

𝑒2∆𝑉𝑖𝑗2𝐴𝑗 − (2𝑒𝜙𝑗 𝐴𝑗 − 2𝑒ℎ𝐵𝑗 )∆𝑉𝑖𝑗 + ℎ2𝐶𝑗 − 2ℎ𝜙𝑗𝐵𝑗 + 𝜙𝑗

2 𝐴𝑗

ℎ2𝐶𝑗𝑑 − 2ℎ𝜙𝑗𝐵𝑗𝑑 + 𝜙𝑗2𝐴𝑗𝑑

(B-14)

To fully evaluate the defined expressions for A, B and C; consider that the

function g(ν), follows a normal distribution of the form;

𝑔(𝜈) =1

𝜎√2𝜋𝑒

− (𝜈− 𝜈)2

2𝜎2 (B-15)

Where ν and 𝜎 are the mean and standard deviation of the distribution

respectively. By making the following simple conversions;

If 𝕏= a+bx ≡ 𝜈− 𝜈

𝜎 , x ≡ 𝜈, a ≡

−𝜈

𝜎, b ≡

1

𝜎 , x =

𝕏−𝑎

𝑏 (B-16)

And using the list of integrals of Gaussian functions as follows;

𝜙(𝕏) = 1

√2𝜋𝑒−

(𝕏)2

2 (B-17)

∫ 𝜙 (𝕏)𝑑𝕏 = 𝜱(𝕏) = 1

2 (1 + 𝑒𝑟𝑓 (

𝕏

√2)) + Constant (B-18)

∫ 𝕏 𝜙 (𝕏) 𝑑𝕏 = −𝜙(𝕏) + Constant (B-19)

∫ 𝕏2 𝜙(𝕏) 𝑑𝕏) = 𝜱(𝕏) − 𝕏 𝜙(𝕏) + Constant (B-20)

Using the defined relationships in Equation B-16 and Equation B-17 to rewrite

Equation B-15, Equation B-19 and Equation B-20 respectively as;

𝑔 (𝑥) = 1

𝜎𝜙(𝕏) (B-21)

∫ 𝑥 𝜙(𝕏) d𝕏 = ∫𝕏−𝑎

𝑏 𝜙(𝕏) d𝕏 =

1

𝑏 ∫(𝕏 − 𝑎) 𝜙(𝕏) d𝕏 =

1

𝑏 (∫ 𝕏 𝜙(𝕏) d𝕏 – a ∫ 𝜙(𝕏) d𝕏)

= 1

𝑏(−𝜙(𝕏) −

𝑎

2 (1 + 𝑒𝑟𝑓 (

𝕏

√2))) (B-22)

And

126

∫ 𝑥2 𝜙(𝕏) d𝕏) = ∫(𝕏−𝑎

𝑏)2 𝜙(𝕏) d𝕏 =

1

𝑏2 ∫(𝕏2 − 2𝕏𝑎 + 𝑎2) 𝜙(𝕏)𝑑𝕏

= 1

𝑏2 (𝜱(𝕏) − 𝕏 𝜙(𝕏) + 2𝑎 𝜙(𝕏) + 𝑎2 𝜱(𝕏)) (B-23)

So that Ai, Bi and Ci can be written as follows for surface i;

𝐴𝑖 = ∫ 𝑔(𝜈) +∞


ℎ

𝑑𝜈 =1

2 (1 + 𝑒𝑟𝑓 (

𝕏

√2))|

+∞𝑒∆𝑉𝑖𝑗+𝜙𝑖

ℎ

(B-24)

𝐵𝑖 = ∫ 𝜈 𝑔(𝜈)+∞


ℎ

𝑑𝜈 = −1

𝑏 (𝜎𝑔(𝑥) +

𝑒

2 (1 + erf (

𝕏

√2)))|

+∞𝑒∆𝑉𝑖𝑗 + 𝜙𝑖

ℎ

(B-25)

𝐶𝑖 = ∫ 𝜈2𝑔(𝜈)+∞


ℎ

𝑑𝜈 =1

𝑏2 ((1 + 𝑒2)1

2(1 + 𝑒𝑟𝑓 (

𝕏

√2)) − (𝕏 − 2𝑒)𝜎𝑔(𝑥))|

+∞𝑒∆𝑉𝑖𝑗+𝜙𝑖

ℎ

(B-26)

Likewise, Aid, Bid 𝑎𝑛𝑑 Cid can be written also for surface i as;

𝐴𝑖𝑑 = ∫ 𝑔(𝜈) +∞

𝜙𝑖ℎ

𝑑𝜈 =

1

2 (1 + 𝑒𝑟𝑓 (

𝕏

√2))|

+∞𝜙𝑖ℎ

(B-27)

𝐵𝑖𝑑 = ∫ 𝜈 𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 = −

1

𝑏 (𝜎𝑔(𝑥) +

𝑒

2 (1 + 𝑒𝑟𝑓 (

𝕏

√2))|

+∞𝜙𝑖ℎ

(B-28)

𝐶𝑖𝑑 = ∫ 𝜈2𝑔(𝜈)+∞

𝜙𝑖ℎ

𝑑𝜈 =

1

𝑏2 ((1 + 𝑒2)1

2(1 + 𝑒𝑟𝑓 (

𝕏

√2)) − (𝕏 − 2𝑒)𝜎𝑔(𝑥))|

+∞𝜙𝑖ℎ

(B-29)

Use −𝑒∆𝑉+𝜙𝑗

ℎ in the limits of 𝐴𝑗, 𝐵𝑗 and 𝐶𝑗 for electrons going in the reverse

direction (��𝑗𝑖).

127

APPENDIX C

CHARGE MEASUREMENT EQUATIONS

The electrostatic force acting on the TM along the x axis, given by 𝐹𝑥 is

𝐹𝑥 = 1

2∑

∂C𝑒

∂𝑥𝑒 (𝑉𝑇𝑀-𝑉𝑒)2

(C-1)

𝐹𝑥 = electrostatic force acting on the TM along the X axis

𝑉𝑇𝑀 = Test Mass (TM) potential

𝑉𝑒 = e-th surface voltage, e = 1, 2, …

𝐶𝑒 = e-th surface capacitance, e = 1, 2, …

𝑉𝑇𝑀 = 𝑞

𝐶𝑇 +

1

𝐶𝑇∑ 𝐶𝑒𝑉𝑒𝑒 (C-2)

A = Amplitude of sinusoidal voltage applied to TM

𝐶𝑇 = total capacitance of the TM toward surrounding surfaces

q = net charge

For charge measurement, set,

𝑉1 = 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡) and 𝑉2 = − 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)

𝑉𝑇𝑀 = 𝑞

𝐶𝑇+

1

𝐶𝑇 (𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)(𝐶1 − 𝐶2)) (C-3)

Substituting Equation C-3 in Equation C-1,

𝐹𝑥 = 1

2 𝜕𝐶1

𝜕𝑥 (

𝑞+ 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)(𝐶1−𝐶2)

𝐶𝑇− 𝐴 𝑐𝑜𝑠(2𝜋𝑓𝑡))2 +

1

2

𝜕𝐶2

𝜕𝑥 (

𝑞+ 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)(𝐶1−𝐶2)

𝐶𝑇 +

𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡))2 (C-4)

Therefore,

𝐹𝑥 =1

2

𝜕𝐶1

𝜕𝑥(

𝑞

𝐶𝑇 − 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)) 2 +

1

2 𝜕𝐶2

𝜕𝑥(

𝑞

𝐶𝑇 + 𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)) 2 (C-5)

If 𝑋+ and 𝑋− indicate the movement of the TM in the positive and negative X

direction respectively with corresponding capacitances of 𝐶𝑋+ and 𝐶𝑋−

towards an

128

opposite surface with area A, then for a TM displaced from the center position by

𝑥 as described by Giacomo Ciani (Diss. Univ. of Trento, 2008)

𝐶𝑋±=

𝜖0𝐴

𝑑∓𝑥 (C-6)

𝜕𝐶𝑋+

𝜕𝑥|

𝑥=0=

𝐶𝑋+

𝑑 (C-7)

𝜕𝐶𝑋−

𝜕𝑥|

𝑥=0=

−𝐶𝑋−

𝑑 (C-8)

If 𝐶1 = 𝐶𝑋− and 𝐶2 = 𝐶𝑋+

and 𝐶1 = 𝐶2, then ∂C2

∂x=

C

d and

∂C1

∂x=

−C

d.

Substituting for 𝐶1 and 𝐶2 in Equation C-5 gives,

𝐹𝑥 = 2𝐶𝑞𝐴 𝑐𝑜𝑠 (2𝜋𝑓𝑡)

𝑑𝐶𝑇 (C-9)

A is the amplitude of sinusoidal voltage applied to the electrodes and q is the net

charge on the TM. For small rotations, the equation of motion of the pendulum is

given by the second order ODE,

�� = −𝜔02𝜑 +

𝐿

𝐼𝐹𝑥 (C-10)

I is the moment of inertia (1.63 × 10−2 kgm2) while L is the arm length (0.22m)

Homogenous solution:

�� + 𝜔02𝜑 = 0 (C-11)

𝜑 = 𝐴 𝑐𝑜𝑠 (𝜔0𝑡) + 𝐵 𝑠𝑖𝑛 (𝜔0𝑡) (C-12)

�� = −𝐴 𝜔0𝑠𝑖𝑛 (𝜔0𝑡) + 𝐵 𝜔0𝑐𝑜𝑠 (𝜔0𝑡) (C-13)

�� = −𝐴 𝜔02𝑐𝑜𝑠 (𝜔0𝑡) − 𝐵 𝜔0

2𝑠𝑖𝑛 (𝜔0𝑡) (C-14)

Substituting Equation C-14 and Equation C-12 into Equation C-11

−𝐴 𝜔𝑜2𝑐𝑜𝑠 − 𝐵 𝜔0

2𝑠𝑖𝑛 (𝜔0𝑡) + 𝜔02(𝐴 𝑐𝑜𝑠 (𝜔0𝑡) + 𝐵 𝑠𝑖𝑛 (𝜔0𝑡)) = 0 (C-15)

So that,

𝜑ℎ = 𝐴 𝑐𝑜𝑠 (𝜔0𝑡) + 𝐵 𝑠𝑖𝑛 (𝜔0𝑡) (C-16)

129

The pendulum is subjected to an external periodic force so the particular solution

is the solution of interest in charge measurements. For the particular solution;

Let;

𝜑𝑝 = 𝐸 𝑐𝑜𝑠 (2𝜋𝑓𝑡) + 𝐹 𝑠𝑖𝑛 (2𝜋𝑓𝑡) (C-17)

��𝑝 = − 2𝜋𝑓 𝐸 𝑠𝑖𝑛 (2𝜋𝑓𝑡) + 2𝜋𝑓 𝐹 𝑐𝑜𝑠 (2𝜋𝑓𝑡) (C-18)

��𝑝 = −(2𝜋𝑓)2 𝐸 𝑐𝑜𝑠 (2𝜋𝑓𝑡) − (2𝜋𝑓)2 𝐹 𝑠𝑖𝑛 (2𝜋𝑓𝑡) (C-19)

��𝑝 + 𝜔02𝜑𝑝 = 𝐷 𝑐𝑜𝑠(2𝜋𝑓𝑡) (C-20)

Substitute Equation C-17 and Equation C-19 into Equation C-20

𝐸(𝜔02𝑐𝑜𝑠 (2𝜋𝑓𝑡) − (2𝜋𝑓)2 𝑐𝑜𝑠 (2𝜋𝑓𝑡)) + 𝐹 (𝜔0

2𝑠𝑖𝑛 (2𝜋𝑓𝑡)

− (2𝜋𝑓)2 𝑠𝑖𝑛 (2𝜋𝑓𝑡))

= 𝐷 𝑐𝑜𝑠(2𝜋𝑓𝑡) (C-21)

Comparing LHS and RHS

𝐹 = 0 (C-22)

𝐸 𝑐𝑜𝑠 (2𝜋𝑓𝑡) (𝜔02 − (2𝜋𝑓)2) = 𝐷 𝑐𝑜𝑠(2𝜋𝑓𝑡) (C-23)

𝐸 = (𝐷

𝜔02− (2𝜋𝑓)2

) (C-24)

From Equation C-10 and Equation C-20,

𝐷 𝑐𝑜𝑠(2𝜋𝑓𝑡) = 𝐿

𝐼𝐹𝑥 (C-25)

𝐷 = 2𝐶𝑞𝐴 𝐿

𝑑𝐶𝑇𝐼 (C-26)

𝐸 =

2𝐶𝑞𝐴 𝐿

𝑑𝐶𝑇𝐼

𝜔02− (2𝜋𝑓)2 (C-27)

Find θp from Equation C-17

130

𝜑𝑝 =

2𝐶𝑞𝐴 𝐿

𝑑𝐶𝑇𝐼

𝜔02− (2𝜋𝑓)2 𝑐𝑜𝑠 (2𝜋𝑓𝑡) (C-28)

The charge q, can be found from the amplitude of 𝜑p as;

𝑞 =𝜑𝑝𝐶𝑇𝐼 (𝜔0

2− (2𝜋𝑓)2)

2𝐶𝑑𝐴𝐿 (C-29)

131

LIST OF REFERENCES

[1] Hulse RA, Taylor JH. Discovery of a pulsar in a binary system. Neutron stars, black holes, and binary X-ray sources. 1975 Aug 31;48: 433. [2] Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K, Adams C, Adams T, Addesso P, Adhikari RX, Adya VB. Observation of gravitational waves from a binary black hole merger. Physical review letters. 2016 Feb 11; 116 (6):061102. [3] Camp JB, Cornish NJ. Gravitational wave astronomy. Annu. Rev. Nucl. Part. Sci.. 2004 Dec 8;54:525-77. [4] Shaul DN, Araújo HM, Rochester GK, Schulte M, Sumner TJ, Trenkel C, Wass P. Charge management for LISA and LISA Pathfinder. International Journal of Modern Physics D. 2008 Jul;17(07):993-1003. [5] Balakrishnan K, Sun KX, Alfauwaz A, Aljadaan A, Almajeed M, Alrufaydah M, Althubiti S, Aljabreen H, Buchman S, Byer RL, Conklin J. UV LED charge control of an electrically isolated proof mass in a Gravitational Reference Sensor configuration at 255 nm. arXiv preprint arXiv:1202.0585. 2012 Feb 3. [6] Ziegler, T., Fichter, W., Schulte, M., & Vitale, S. (2009). Principles, operations, and expected performance of the LISA Pathfinder charge management system. In Journal of Physics: Conference Series (Vol. 154, No. 1, p. 012009). IOP Publishing. [7] Ziegler, T., Bergner, P., Hechenblaikner, G., Brandt, N., & Fichter, W. (2014). Modeling and performance of contact-free discharge systems for space inertial sensors. Aerospace and Electronic Systems, IEEE Transactions on, 50(2), 1493-1510. [8] Hollington, Daniel. The charge management system for LISA and LISA Pathfinder. Diss. Imperial College London, 2011. [9] Oshima, C., Aono, M., Tanaka, T., Kawai, S., Zaima, S., & Shibata, Y. (1981). Clean TiC (001) surface and oxygen chemisorption studied by work function measurement, angle-resolved X-RAY photoelectron spectroscopy, ultraviolet photoelectron spectroscopy and ion scattering spectroscopy. Surface Science, 102(2-3), 312-330. [10] Authors III/17A-22A-41A1b and Editors of the LB Volumes. Silicon carbide (SiC),

work function. SpringerMaterials - The Landolt-Bornstein Database. [11] Ciani, Giacomo. Free-fall of LISA Test Masses: a new torsion pendulum to test translational acceleration. Diss. Univ. of Trento, 2008. [12] Chilton, A., Shelley, R., Olatunde, T., Ciani, G., Conklin, J. W., & Mueller, G. (2015). The UF Torsion Pendulum, a LISA Technology Testbed: Sensing System and Initial Results. In Journal of Physics: Conference Series (Vol. 610, No. 1, p. 012038). IOP Publishing.

132

[13] Hollington, D., Baird, J. T., Sumner, T. J., & Wass, P. J. (2015). Characterising and testing deep UV LEDs for use in space applications. Classical and Quantum Gravity, 32(23), 235020. [14] Ciani, G., Chilton, A., Apple, S., Olatunde, T., Aitken, M., Mueller, G., & Conklin, J. W. (2017). A new torsion pendulum for gravitational reference sensor technology development. Review of Scientific instruments, 88(6), 064502. [15] Olatunde, T., Shelley, R., Chilton, A., Serra, P., Ciani, G., Mueller, G., & Conklin, J. (2015). 240 nm UV LEDs for LISA test mass charge control. In Journal of Physics: Conference Series (Vol. 610, No. 1, p. 012034). IOP Publishing. [16] LISA L3 mission proposal

[17] Hechenblaikner, G., Ziegler, T., Biswas, I., Seibel, C., Schulze, M., Brandt, N & Reinert, F. T. (2012). Energy distribution and quantum yield for photoemission from air-contaminated gold surfaces under ultraviolet illumination close to the threshold. Journal of Applied Physics, 111(12), 124914. [18] Mekhalif, Z., J. Riga, J-J. Pireaux, and J. Delhalle. "Self-assembled monolayers of n-dodecanethiol on electrochemically modified polycrystalline nickel surfaces." Langmuir 13, no. 8 (1997): 2285-2290. [19] Laulainen, J., Kalvas, T., Koivisto, H., Komppula, J., & Tarvainen, O. (2015, April). Photoelectron emission from metal surfaces induced by VUV-emission of filament driven hydrogen arc discharge plasma. In AIP Conference Proceedings (Vol. 1655, No. 1, p. 020007). AIP Publishing. [20] Robertson, N. A., Blackwood, J. R., Buchman, S., Byer, R. L., Camp, J., Gill, D., ... & Zhou, P. (2006). Kelvin probe measurements: investigations of the patch effect with applications to ST-7 and LISA. Classical and Quantum Gravity, 23(7), 2665. [21] Schulte, M. O., Shaul, D. N. A., Hollington, D., Waschke, S., Sumner, T. J., Wass, P. J., & Nannarone, S. (2009). Inertial sensor surface properties for LISA Pathfinder and their effect on test mass discharging. Classical and Quantum Gravity, 26(9), 094008. [22] Gottfried, J. M., Schmidt, K. J., Schroeder, S. L. M., & Christmann, K. (2003). Adsorption of carbon monoxide on Au (1 1 0)-(1× 2). Surface science, 536(1-3), 206-224. [23] Johnson, P. B., & Christy, R. W. (1972). Optical constants of the noble metals. Physical review B, 6(12), 4370. [24] ADN8831 datasheet; https://www.digikey.com/number/en/analog-devices-inc/505/ADN8831/38766

https://www.digikey.com/number/en/analog-devices-inc/505/ADN8831/38766

https://www.digikey.com/number/en/analog-devices-inc/505/ADN8831/38766

133

[25] Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.X. and Adya, V.B., 2016. Observation of gravitational waves from a binary black hole merger. Physical review letters, 116(6), p.061102. [26] Livas, J., & Moore, B. (1989). LIGO vacuum system study. The Journal of Environmental Sciences, 32(6), 28-32. [27] https://www.ligo.caltech.edu/LA/page/ligo-technology

[28] Schulte, M. O., D. N. A. Shaul, D. Hollington, S. Waschke, T. J. Sumner, P. J. Wass, Luca Pasquali, and Stefano Nannarone. "Inertial sensor surface properties for LISA Pathfinder and their effect on test mass discharging." Classical and Quantum Gravity 26, no. 9 (2009): 094008.

[29] Ciani, G., Chilton, A., Apple, S., Olatunde, T., Aitken, M., Mueller, G., & Conklin, J. W. (2017). A new torsion pendulum for gravitational reference sensor technology development. Review of Scientific instruments, 88(6), 064502. [30] Armano, M., Audley, H., Auger, G., Baird, J., Binetruy, P., Born, M., . & Cavalleri, A. (2015). The LISA pathfinder mission. In Journal of Physics: Conference Series (Vol. 610, No. 1, p. 012005). IOP Publishing. [31] Thorpe, J. I., C. J. Cutler, M. Hewitson, O. Jennrich, P. Maghami, S. Paczkowski, G. Russano, S. Vitale, and W. J. Weber. "Free-flight experiments in LISA Pathfinder." (2014). [32] Giusteri, Roberta, and LPF collaboration. "The free-fall mode experiment on LISA Pathfinder: first results." In Journal of Physics: Conference Series, vol. 840, no. 1, p. 012005. IOP Publishing, 2017. [33] Ammann, M. (2000). X-ray Photoelectron Spectroscopy (XPS).

https://www.ligo.caltech.edu/LA/page/ligo-technology

134

BIOGRAPHICAL SKETCH

Taiwo J. Olatunde was born in Lagos, Nigeria. She obtained her BS. in

mechanical engineering at the University of Lagos, Nigeria in 2010 and a master’s

degree in aerospace engineering at the University of Florida in 2013, She graduated

with a PhD in aerospace engineering at the University of Florida in 2018. Taiwo is

married to Yomi Olatunde and is a mother to two children, Mayowa Katherine and

Ayomide Joanne.

UV LED BASED CHARGE CONTROL FOR THE LISA …

Documents

Transcript of UV LED BASED CHARGE CONTROL FOR THE LISA …